Calculate the simple interest on the following:
An investment of \$8760 at 2\% p.a. for 7 years.
A loan of \$8000 at 8\% p.a. for 6 years.
An investment of \$4640 at a rate of 2\% p.a. for 23 months.
Beth takes out a car loan of \$3000 at a simple interest rate of 8\% p.a. She plans to repay the loan over 4 years through regular monthly repayments.
Calculate the total interest that Beth will incur over the duration of the repayments.
Calculate the value of each repayment of the loan.
The recurrence relation which models the value of the investment after {n + 1} months is given by V_{n + 1} = V_n + 11.5, V_0 = 1150.
Is the investment type simple interest or compound interest?
What is the annual interest rate?
Determine the balance of the account after 8 years.
The recurrence relation which models the value of the investment after n + 1 years is given by V_{n + 1} = V_n + 350, V_0 = 5000.
Is the investment type simple interest or compound interest?
What is the annual interest rate?
Determine the balance of the account after 5 years.
Sunil lives in India and invests 54\,000 INR into an investment account that pays 5.6\% simple interest per annum.
By what amount will the account increase each year?
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 4 years.
Determine how many whole years it takes for the balance to exceed 94\,824 INR.
A retiree invests \$570\,500 into an investment account that pays 6\% simple interest per annum.
By what amount will the account increase each year?
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 13 years.
Determine how many whole years it takes for the balance to exceed 1.5 million dollars.
An investor deposits \$74\,000 into an investment account that pays 3.7\% simple interest per annum.
By what amount will the account increase each year?
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 9 years.
Determine how many whole years it takes for the balance to exceed \$116\,439.
Abbey invests \$2700 into a private savings fund that pays 5.7\% simple interest per annum.
By what amount will the investment fund increase each year?
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 5 years.
Determine how many whole years it takes for the balance to exceed \$7393.95.
An investor deposits \$51\,000 into a high risk fund that pays 0.3\% simple interest per month.
By what amount will the investment fund increase each month?
Write the recurrence relation for this situation where n is the number of months.
Write the explicit rule that can be used to find the balance at the end of n months.
Determine the balance after 9 years.
Determine how many whole months it takes for the balance to exceed \$54\,289.5.
Explain how compound interest is earned over the course of an investment.
\$3000 is invested at 4\% p.a., compounded annually. The table below tracks the growth of the principal over three years.
| Time Period (years) | Value at beginning of time period | Value at end of time period | Interest earned in time period |
|---|---|---|---|
| 1 | \$3,000 | A | B |
| 2 | C | \$3,244.80 | D |
| 3 | \$3,244.80 | \$3,374.59 | E |
Find the value of:
Find the total interest earned over the three years.
A \$2090 investment earns interest at 4.2\% p.a. compounded annually over 17 years. Use the compound interest formula to calculate the value of this investment.
A \$3710 investment earns interest at 4.8\% p.a. compounded quarterly over 13 years. Use the compound interest formula to calculate the value of this investment.
Sally's investment of \$8950 earns interest at 4\% p.a. compounded annually over 4 years. Find the amount of interest earned.
Luke's investment of \$2000 earns interest at 5\% p.a, compounded annually over 3 years.
Find the value of the investment after 3 years.
Find the amount of interest earned.
Rosey borrows \$13\,000 at an interest rate of 2.5\% p.a. compounded weekly. If she makes no repayments, use the finance application on your CAS calculator to find the amount of interest that is owed after 3 years. Assume there are 52 weeks in a year.
\$3700 is invested for three years at a rate of 7\% p.a. compounding annually. The balance and interest earned for the first two years is shown in the table:
Find the value of:
Calculate the total interest earned over the three years.
| Balance | Interest earned | |
|---|---|---|
| First year | \$3,700 | \$259 |
| Second year | \$3,959 | \$277.13 |
| Third year | A | B |
| Fourth year | C | - |
\$13\,000 is borrowed at an interest rate of 2.7\% p.a. compounded semi-annually. Use the finance application on your CAS calculator to find how much is owed after 4.5 years.
In 2001, the price of a bottle of orange juice was \$3.20. Find the price of a bottle of orange juice in 2006 if the inflation rate was 8\% p.a.?
For each of the following investments defined by their annual interest rates and their corrresponding recurrence relations:
State whether the investment type simple interest or compound interest.
3.72\% p.a., modelled by the recurrence relation P_{n + 1} = P_n \times 1.0031, P_0 = 1200
2.04\% p.a., modelled by the recurrence relation P_{n + 1} = P_n \times 1.0051, P_0 = 1400
6.24\% p.a., modelled by the recurrence relation P_{n + 1} = P_n \times 1.0012, P_0 = 1500
The recurrence relation which models the yearly growth of an investment after n + 1 years is given by P_{n + 1} = P_n \times 1.08, P_0 = 1100.
Is the investment type simple interest or compound interest?
Find the annual interest rate
Determine the balance of the account after 8 years.
The recurrence relation which models the monthly growth of an investment after n + 1 months is given by P_{n + 1} = P_n \times 1.005, P_1 = 1206.
Is the investment type simple interest or compound interest?
Find the annual interest rate.
State the initial amount that was invested.
The balance of an investment at the end of the nth year where interest is compounded annually is given by A_n = 1.061 A_{n - 1}, A_0 = 15\,000.
State the annual interest rate.
State the amount invested.
Determine the balance at the end of the first year.
Use the sequences facility on your calculator to determine the balance at the end of 20 years.
The balance of an investment at the beginning of each quarter where interest is compounded quarterly is given by A_n = 1.02 A_{n - 1}, A_1 = 5000.
State the quarterly interest rate.
State the nominal annual interest rate.
Use the sequences facility on your calculator to determine the balance at the beginning of the second year.
Use the sequences facility on your calculator to determine the balance at the end of the second year.
The balance of an investment at the end of each month where interest is compounded monthly is given by A_n = 1.015 A_{n - 1}, A_0 = 2000. The investment began at the beginning of January 2010.
State the monthly interest rate.
Use the sequences facility on your calculator to determine the balance at the end of the first year.
Use the compound interest formula to determine the balance at the end of the first year to confirm the answer from the previous part.
Use the sequences facility on your calculator to determine in which month and year the investment is worth double the initial amount invested.
\$3900 is invested for three years at a rate of 10\% per annum, compounding annually. The balance and interest for the first two years are shown in the table:
Write the recurrence relation for this situation.
Use the sequence facility of your calculator to find the value of:
Calculate the total interest earned over the three years.
| Balance | Interest earned | |
|---|---|---|
| First year | \$3,900 | \$390 |
| Second year | \$4,290 | \$429 |
| Third year | \$A | \$B |
| Fourth year | \$C | - |
\$8000 is invested at 6\% p.a., compounded annually.
Write the recurrence relation for this situation.
Using the sequence facility of your calculator, complete the following table:
| Time Period (years) | Value at beginning of time period | Value at end of time period | Interest earned in time period |
|---|---|---|---|
| 1 | \$8,000 | ||
| 2 | \$8,988.80 | ||
| 3 | \$8,988.80 | \$9,528.13 |
Find the total interest earned over the three years.
The value of land which is currently priced at \$520 per square metre, is expected to grow by 7.9\% each year for the next 4 years.
Write the recurrence relation for this situation.
Using the sequence facility of your calculator, find how much will the land cost at the end of 4 years.
Callum invests \$5700 into an investment account that pays 3.2\% per annum, compounded annually.
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write an explicit rule that can be used to find the balance at the end of n years.
Use the sequences application on your calculator to determine the balance after 9 years.
Determine how many whole years it takes for the balance to exceed \$10\,208.
Erica invests \$50\,000 into an investment account that pays 2.8\% per annum, compounded annually.
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Write an explicit rule that can be used to find the balance at the end of n years.
Use the sequences application on your calculator to determine the balance after 21 years.
Determine how many whole years it takes for the balance to exceed \$109\,843.
Juan invests \$25\,000 into an investment account that pays 1.8\% compound interest per annum, compounded quarterly.
Find the quarterly interest rate.
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth quarter and t_0 is the initial investment.
Write an explicit rule that can be used to find the balance at the end of n quarters.
Use the sequences application on your calculator to determine the balance after 6 years.
Determine how many whole years it takes for the balance to exceed \$28\,800.
Rani invests 27\,500 INR into an investment account that pays 6.3\% compound interest per annum, compounded monthly.
Find the monthly interest rate.
Write the recurrence relation for this situation, where t_n is the balance at the end of the nth month and t_0 is the initial investment.
Write an explicit rule that can be used to find the balance at the end of n months.
Use the sequences application on your calculator to determine the balance after 4 years.
Determine how many whole months it takes for the balance to exceed 35\,543 INR.
Convert your answer from part (e) to years. Round your answer to two decimal places.
Briony invests \$29\,000 into an investment account that pays 2.2\% compound interest per annum.
Complete the recurrence relation for this situation, where t_n describes the value of the investment after the nth year.
Write an explicit rule that can be used to find the balance at the end of n years.
Use the sequences application on your calculator to determine the balance after 5 years.
Determine how many whole years it takes for the balance to exceed \$41\,527.
For each of the following investments:
Find how much money is in the account at the end of the first year.
Write a recursive rule, V_n, that gives the balance in the account at the end of year n.
\$5000 is invested at the beginning of the year in an account that earns 3\% per annum interest, compounded annually.
\$3000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded annually.
\$2000 is invested at the beginning of the year in an account that earns 4\% per annum interest, compounded quarterly.
\$4000 is invested at the beginning of the year in an account that earns 8\% per annum interest, compounded quarterly.
\$5000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded monthly.
\$3000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded monthly.
Han opened a savings account at the beginning of February 2015, where the interest is compounded monthly. His statements for March, April and May show his account balance at the beginning of each month:
Find the monthly interest rate r of his investment.
Calculate the nominal annual interest rate of his investment.
How much did Han deposit into this savings account when he opened it?
| Balance | |
|---|---|
| March | \$2,550 |
| April | \$2,601 |
| May | \$2,653.02 |
Write a recursive rule, V_n, that gives the balance in the account at the beginning of the nth month.
Maria opened a savings account at the beginning of April 2014, where the interest is compounded quarterly. Her statements for June, September and December show her account balance at the beginning of each quarter:
Find the quarterly interest rate of her investment.
Calculate the nominal annual interest rate of her investment.
How much did Maria deposit into this savings account?
| Balance | |
|---|---|
| June | \$7,800 |
| September | \$8,112 |
| December | \$8,436.48 |
Write a recursive rule, V_n, that gives the balance in the account at the end of the nth quarter.
The following spreadsheet shows the balance (in dollars) in a savings account in 2014, where interest is compounded monthly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Month} | \text{Balance at beginning of month} | \text{Interest} | \text{Balance at end of month} |
| 2 | \text{July} | 8,000 | 160 | X |
| 3 | \text{August} | 8,160 | 163.20 | 8,323.20 |
| 4 | \text{September} | 8,323.20 | Y | 8,489.66 |
| 5 | \text{October} | Z | 169.79 | 8,659.45 |
| 6 | \text{November} | 8,659.45 | 173.19 | 8,832.64 |
Calculate the value of X.
Calculate the monthly interest rate.
Calculate the value of Y.
Calculate the value of Z.
Write a recursive rule, B_n, that gives the balance at the end of the nth month, with July being the first month.
Write an explicit rule for B_n, the balance at the end of the nth month, with July being the first month.
The following spreadsheet shows the balance (in dollars) in a savings account in 2013, where interest is compounded quarterly.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Quarter} | \text{Balance at beginning of quarter} | \text{Interest} | \text{Balance at end of quarter} |
| 2 | 1 | Z | 60 | 3,060 |
| 3 | 2 | 3,060 | Y | 3,121.20 |
| 4 | 3 | 3,121.20 | 62.42 | X |
| 5 | 4 | 3,183.62 | 63.67 | 3,247.29 |
Calculate the value of X.
Calculate the quarterly interest rate to two decimal places.
Calculate the value of Y.
Calculate the nominal annual interest rate.
Calculate the value of Z.
Write a recursive rule, B_n, that gives the balance at the beginning of the nth quarter.
Write an explicit rule for B_n, the balance at the beginning of the nth quarter.
The following spreadsheet shows the balance (in dollars) in a savings account in 2014, where interest is compounded monthly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Month} | \text{Balance at beginning of month} | \text{Interest} | \text{Balance at end of month} |
| 2 | \text{January} | 1000 | 20 | 1020 |
| 3 | \text{February} | 1020 | 20.40 | 1040.40 |
| 4 | \text{March} | 1040.40 | 20.81 | 1061.21 |
| 5 | \text{April} | 1061.21 | 21.22 | 1082.43 |
| 6 | \text{May} |
Use the numbers for January to calculate the monthly interest rate.
Fill in the row for May.
Write a recursive rule, B_n, that gives the balance at the beginning of the nth month of 2014.
Use the sequences facility on your calculator to determine the balance at the end of this year.
Calculate the total amount of interest earned over the year.
The following spreadsheet shows the balance (in dollars) in a savings account in 2012, where interest is compounded quarterly:
| A | B | C | D | |
|---|---|---|---|---|
| 1 | \text{Quarter} | \text{Balance at beginning of quarter} | \text{Interest} | \text{Balance at end of quarter} |
| 2 | 1 | 6,000 | 120 | 6,120 |
| 3 | 2 | 6,120 | 122.40 | 6,242.40 |
| 4 | 3 | 6,242.40 | 124.85 | 6,367.25 |
| 5 | 4 |
Calculate the quarterly interest rate.
Fill in the row for quarter 4.
Write a recursive rule, B_n, that gives the balance at the end of the nth quarter after the beginning of 2012.
Use the sequences facility on your calculator to determine the balance at the beginning of the 3rd year.
How many whole quarters after the beginning of 2012 will the balance be double the initial investment of \$6000?
The recurrence relation which models the daily growth of an investment after n + 1 days is given by P_{n + 1} = P_n \times 1.0001, P_0 = 300. Assume there are 365 days in a year.
Is the investment type simple interest or compound interest?
Find the annual interest rate.
State the initial amount that was invested.
Determine the balance of the account after 1 year.
The balance of an investment at the end of the nth year where interest is compounded annually is given by P_n = 1.023 P_{n - 1}, P_0 = 5100.
State the annual interest rate.
State the initial amount that was invested.
Determine the balance at the end of the first year.
Use the sequences facility on your calculator to determine the balance at the end of 30 years.
Calculate the amount of interest earned over the 30 years.
The balance of an investment,, at the end of the nth year where interest is compounded annually is given by A_n = 1.051 A_{n - 1}, A_0 = 20\,000.
State the annual interest rate.
State the amount invested.
Determine the balance at the end of the first year.
Use the sequences facility on your calculator to determine the balance at the end of 10 years.
Calculate the amount of interest earned over the 10 years.
The balance of an investment at the end of the nth month where interest is compounded monthly is given by M_n = 1.0012 M_{n - 1}, M_1 = 1601.92.
State the monthly interest rate.
Hence find the annual interest rate.
State the value of the investment at the end of the first month.
Hence find the amount invested.
Determine the balance at the end of the first year.
Use the sequences facility on your calculator to determine the balance at the end of 8 years.
The balance of an investment at the end of the n + 1th quarter where interest is compounded quarterly is given by Q_{n + 1} = 1.007 Q_n, Q_1 = 8660.20.
Find the annual interest rate.
State the value of the investment at the end of the first quarter.
Hence find the amount invested.
Determine the balance at the end of the first year.
Use the sequences facility on your calculator to determine the balance at the end of 8 years.
Calculate the amount of interest earned over the 8 years.
Christa invested \$7080 at 7\% p.a., compounded annually over 3 years.
Use the sequences application on your calculator to find the following:
The recurrence relation for this situation.
The interest for the first year.
The total amount invested after the first year.
The interest for the second year.
The total amount invested after the second year.
The interest for the third year.
The total amount invested after the third year.
The total amount of interest earned over the 3 years.
The interest as a percentage of the initial investment, to two decimal places.
The simple interest earned after 3 years, if the interest was calculated using a flat rate of 7\% p.a.
How much more compound interest than simple interest would have accumulated over these 3 years.
Chantelle invested \$8620 at 8\% p.a., compounded annually over 3 years.
Use the sequences application on your calculator to find the following:
The interest for the first year.
The total amount of the investment after the first year.
The interest for the second year.
The total amount invested after the second year.
The interest for the third year.
The total amount invested after the third year.
The total amount of interest earned over the 3 years.
The interest as a percentage of the initial investment, to two decimal places.
The simple interest earned after 3 years, if the interest was calculated using a flat rate of 8\% p.a.
How much more compound interest than simple interest would have accumulated over these 3 years.
Mae invested \$1800 at 6\% p.a., compounded annually over 3 years.
Use the sequences application on your calculator to find the following:
The recurrence relation for this situation.
The interest for the first year.
The total amount of the investment after the first year.
The interest for the second year.
The total amount invested after the second year.
The interest for the third year.
The total amount invested after the third year.
The total amount of interest earned over the 3 years.
The interest as a percentage of the initial investment, to two decimal places.
The simple interest earned after 3 years, if the interest was calculated using a flat rate of 6\%p.a.
How much more compound interest than simple interest would have accumulated over these 3 years.