If \$16\,716 of simple interest was earned in 7 years, find how much interest was earned:
Each year
Each month
Assuming that a year has 365 days and 52 weeks, calculate the simple interest earned on the following investments:
\$2540 at 9\% p.a. for 2 years.
\$2010 at a rate of 6\% p.a. for 13 months.
\$1050 at a semiannual rate of 1.1\% for 9 years.
\$7000 at 1.8\% per quarter for 9 years.
\$5320 at 6\% p.a. for 95 weeks.
\$5440 at 6\% p.a. for 566 days.
Calculate the simple interest on a loan of \$8000 at 8\% p.a. for 6 years. Give your answer to the nearest dollar.
Tara takes out a car loan of \$6000 at a simple interest of 8\% p.a. She plans to repay the loan over 2 years through regular monthly repayments.
Calculate the total interest that Tara will incur over the duration of the repayment.
Calculate the value of each repayment of the loan. Round your answer to two decimal places if necessary.
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?
Find 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?
Find the annual interest rate.
Determine the balance of the account after 5 years.
Manpreet lives in India and invests 46\,000 INR into an investment account that pays 6.6\% simple interest per annum.
By what amount will the account increase each year?
Write the recurrence relation for Manpreet's situation, where t_n is the balance at the end of the nth year and t_0 is the initial investment.
Find 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 86\,986 INR.
A retiree invests \$540\,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.
Find the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 11 years.
Determine how many whole years it takes for the balance to exceed 1.5 million dollars.
An investor deposits \$77\,000 into an investment account that pays 3.5\% 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.
Find the explicit rule that can be used to find the balance at the end of n years.
Determine the balance after 7 years.
Determine how many whole years it takes for the balance to exceed \$121\,468.
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.
Find 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.
Find 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 \$54289.5.
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.
Complete the table:
| Time Period (years) | Value at beginning of time period | Value at end of time period | Interest earned in time period |
|---|---|---|---|
| 1 | \$3000 | ||
| 2 | \$3244.80 | ||
| 3 | \$3244.80 | \$3374.59 |
Calculate the total interest earned over the three years.
A \$2090 investment earns interest at 4.2\% p.a., compounded annually over 17 years. Calculate the value of this investment.
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.
Sally's investment of \$8950 earns interest at 4\% p.a. compounded annually over 4 years. Calculate the amount of interest earned.
\$3700 is invested for three years at a rate of 7\% p.a., compounding annually. The balance and interest for the first two years are shown in the table:
Find the values of the following:
A
B
C
Calculate the total interest earned over the three years.
| Balance | Interest earned | |
|---|---|---|
| First year | \$3700 | \$259 |
| Second year | \$3959 | \$277.13 |
| Third year | A | B |
| Fourth year | C | - |
In 2001, the price of a bottle of orange juice was \$3.20. What was the price of a bottle of orange juice in 2006 if the inflation rate was 8\% p.a.?
Sharon has \$25\,000 that she wishes to invest for a period of time without touching it. She chooses to invest this money in an account offering 4.25\% p.a. compound interest.
Calculate the value of the investment in dollars after 7 years if interest is compounded monthly.
Calculate the number of years required to double her investment if interest is compounded daily. Round your answer to two decimal places. Assume there are 365 days in a year.
The balance of an investment, in dollars, 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, in dollars, 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, in dollars, 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 and 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 | \$8000 | ||
| 2 | \$8988.80 | ||
| 3 | \$8988.80 | \$9528.13 |
Calculate 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.
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.
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.
Determine the quarterly interest rate.
Write the recurrence relation for this situation.
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 quarters it takes for the balance to exceed \$28\,800.
Convert your answer from part (e) to years.
Rani invests 27\,500 INR into an investment account that pays 6.3\% compound interest per annum, compounded monthly.
Calculate the monthly interest rate.
Write the recurrence relation for this situation.
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, correct to two decimal places.
Briony invests \$29\,000 into an investment account that pays 2.2\% compound interest per annum.
Write the recurrence relation for this situation.
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.
\$5000 is invested at the beginning of the year in an account that earns 3\% per annum interest, compounded annually.
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.
\$3000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded annually.
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 beginning of year n.
\$2000 is invested at the beginning of the year in an account that earns 4\% per annum interest, compounded quarterly.
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 the nth quarter.
\$4000 is invested at the beginning of the year in an account that earns 8\% per annum interest, compounded quarterly.
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 beginning of the nth quarter.
\$5000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded monthly.
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 the nth month.
\$3000 is invested at the beginning of the year in an account that earns 6\% per annum interest, compounded monthly.
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 beginning of the \\nth month.
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.
Calculate 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?
| Month | Balance |
|---|---|
| \text{March} | \$2550 |
| \text{April} | \$2601 |
| \text{May} | \$2653.02 |
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.
Calculate the quarterly interest rate r of her investment.
Calculate the nominal annual interest rate of her investment.
How much did Maria deposit into this savings account?
| Month | Balance |
|---|---|
| \text{June} | \$7800 |
| \text{September} | \$8112 |
| \text{December} | \$8436.48 |
Write a recursive rule, V_n, that gives the balance in the account at the end of the nth quarter.
The following table 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} | 8000 | 160 | X |
| 3 | \text{August} | 8160 | 163.20 | 8323.20 |
| 4 | \text{September} | 8323.20 | Y | 8489.66 |
| 5 | \text{October} | Z | 169.79 | 8659.45 |
| 6 | \text{November} | 8659.45 | 173.19 | 8832.64 |
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 table 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 | 3060 |
| 3 | 2 | 3060 | Y | 3121.20 |
| 4 | 3 | 3121.20 | 62.42 | X |
| 5 | 4 | 3183.62 | 63.67 | 3247.29 |
Calculate the value of X.
Calculate the quarterly interest rate, correct 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.
Neil and John both inherit \$12\,000 and put their money in compound interest-bearing accounts for a period of 5 years.
Neil places his money in an account with an interest rate of 2.75\% p.a. compounded monthly:
| \text{Number of months} | 1 | 2 | 3 | ... | 60 |
|---|---|---|---|---|---|
| \text{Value of investment }(\$) | 12\,027.50 | A | B | ... | 13\,766.65 |
Find the values of the following:
A
B
Write a recursive rule for Neil's investment V_{n + 1} in terms of V_n, where V_n describes the value of the investment after the nth month (in exact form) and the initial investment V_0.
John places his money in an account which earns interest compounded daily. At the end of the five years, John’s balance is the same as Neil’s balance. Calculate the interest rate per annum for John’s investment account as a percentage. Round your answer to three decimal places. Assume there are 365 days in a year.
Does the difference in compounding periods mean that John’s interest rate per annum is higher or lower than Neil’s?
The following table 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} |
Calculate the monthly interest rate.
Complete 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 table 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 | 6000 | 120 | 6120 |
| 3 | 2 | 6120 | 122.40 | 6242.40 |
| 4 | 3 | 6242.40 | 124.85 | 6367.25 |
| 5 | 4 |
Calculate the quarterly interest rate.
Complete 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 table below gives the account balance of an investment after each week:
Calculate the weekly interest rate as a percentage.
Write the recursive rule for the investment B_{n + 1} in terms of B_n, where B_n describes the value of the investment after the nth week. Include the initial investment B_0.
Hence, find the values of the following:
If interest was to be calculated weekly and added to the account monthly, would the balance be higher, lower or the same after 4 years?
If the interest rate was doubled, what would the effect be on the amount of interest earned?
| Week | Balance |
|---|---|
| 0 | 15\,000 |
| 1 | 15\,675 |
| 2 | 16\,380.38 |
| 3 | 17\,117.49 |
| 4 | 17\,887.78 |
| 5 | 18\,692.73 |
| 6 | X |
| ... | ... |
| 45 | Y |
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.
How much more compound interest than simple interest would have accumulated over these 3 years.
Christa 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.
How much more compound interest than simple interest would have accumulated over these 3 years.