Find the future value of the following loans:
\$13\,000 is borrowed at an interest rate of 2.5\% p.a. compounded semi-annually for 3.5 years.
\$2000 is borrowed at an interest rate of 12\% p.a. compounded monthly for 2 years.
\$5000 is borrowed at an interest rate of 3.5\% p.a. compounded daily for 4 years.
\$500 is borrowed at an interest rate of 10.7\% p.a. compounded daily for 10 weeks.
\$2000 is borrowed at an interest rate of 1.6\% per quarter compounded quarterly for 4 years.
Find the future value of the following investments:
\$3000 is invested at an interest rate of 5\% p.a. compounded annually for 17 years.
\$3000 is invested at an interest rate of 4\% p.a. compounded quarterly for 17 years.
\$6000 is invested at an interest rate of 2.5\% p.a. compounded monthly for 3.5 years.
\$10\,000 is invested at an interest rate of 2.7\% p.a. compounded monthly for 18 months.
\$15\,000 is invested with at an interest rate of 0.7\% per month compounded monthly for 23 months.
Ryan borrows \$4000 at a rate of 5.5\% p.a. compounded weekly. Assuming he makes no repayments, find how much he owes after 1 year.
Skye takes out a car loan of \$32\,000 at an interest rate of 0.01\% per day compounded monthly.
Find the interest rate per month. Give your answer as a percentage to three decimal places. Assume that there are 365 days in a year.
If she makes no repayments, find how much Skye owes after 5 years.
\$2000 is invested at an interest rate of 4\% p.a. compounded quarterly.
Find the value of the investment after 15 years.
Find the amount of interest earned over the 15 years.
\$5000 is borrowed at an interest rate of 12\% p.a. compounded monthly:
Find the amount owed after 3 years.
Find the amount of interest accrued over the 3 years.
Find the amount of interest that is earned on the following accounts:
\$10\,000 is invested at an interest rate of 2.5\% p.a. compounded monthly over 24 months.
\$11\,000 is borrowed at an interest rate of 3.5\% p.a. compounded semi-annually over 30 months.
\$900 is borrowed at an interest rate of 10.5\% p.a. compounded monthly over 1.5 years.
\$24\,000 is deposited in a savings account which attracts interest at 1.3\% p.a. compounded daily over 9 years. Assume 365 days in a year.
\$12\,000 is invested at an interest rate of 0.4\% per month compounded monthly over 4.5 years.
Nadia borrows \$12\,000 at an interest rate of 3.5\% p.a. compounded weekly. If she makes no repayments, find the amount of interest that is owed after 3 years.
Luke borrows \$700 at an interest rate of 17\% p.a. compounded daily. Find the amount of interest that is owed after two weeks.
Harry borrows \$3300 at a monthly rate of 1.2\% compounded daily. If he pays back the money after one month, find the amount of interest that Harry paid.
Katrina has her property investment currently valued at \$750\,000 and she knows that its value increased at a rate of 10\% p.a. compounded annually for the last 20 years. Find the value of her investment at the beginning of the 20 years.
The final amount owed on a 30-year loan at 4.5\% p.a. compounded annually is \$240\,000.
Find the original amount of the loan.
Find the amount of interest paid on the loan.
A savings account has a balance of \$25\,500 after 10 years of interest at 1.6\% p.a. compounded annually. Find the initial deposit.
Harry expects to receive a Christmas bonus of \$7000 in 6 months time. His credit card incurs interest at 14\% p.a. compounded weekly with no interest free period. What is the most he can spend now using his credit card and still be able to pay it off using his Christmas bonus? Assume 52 weeks in a year.
Jack is aiming to save \$35\,000 after 10 years of investing at an interest rate of 0.1\% per week compounded monthly. Find the amount he needs to deposit as a principal. Assume 52 weeks in a year.
Laura has a choice between a high-risk investment which attracts interest at 10\% p.a. compounded annually, or a low-risk investment at 5\% p.a. compounded annually. She has \$50\,000 to invest and her goal is to grow it to \$60\,000 within 3 years.
Which of the investments would allow her to reach her goal, the high risk or the low risk investment?
Homer signs up for a loan of \$1000 compounded annually. After 3 years, he owes \$2500. What interest rate has the bank been applying per annum? Round your answer to one decimal place.
Sharon discovers a credit card debt of \$2100 from a \$1000 purchase she made 2.5 years prior. Assuming the interest was compounded monthly, what interest rate has been applied per annum? Round your answer to the nearest percentage.
A \$2000 investment grows to \$4000 over 2 years accumulating interest compounded monthly. Calculate the interest rate per annum that is being applied. Round your answer to one decimal place.
What interest rate per annum would be required to double an investment of \$1000 in 2 years, if the interest is compounded daily? Round your answer to one decimal place. Assume there are 365 days in a year.
\$1000 is placed in a term deposit with a rate of 5\% p.a. compounded annually. How many whole years will it take for the balance to increase in value to at least \$1500?
Vanessa borrows \$25\,000 at an interest rate of 4.3\% p.a. compounded annually to pay for her university degree. If she continues into postgraduate study, how many whole years will it take for her debt to reach at least \$40\,000?
Nadia invests \$1200 in a term deposit with a rate of 2.3\% p.a. compounded monthly. How many whole months will it take for the investment to increase in value to at least \$1500?
Ryan borrows \$800 from the bank at a rate of 0.2\% per week, compounded weekly. How many whole weeks will it take for the amount he owes to increase to at least \$1300? Assume 52 weeks in a year.
Neil invests \$900 in a term deposit with a rate of 2.3\% p.a. compounded daily. How many years will it take for the investment to at least double in value? Assume 365 days in a year.
What interest rate per annum would be required to double an investment of \$P in 4 years if the interest is compounded quarterly? Round your answer to one decimal place.
How many whole years will it take an investment of \$P to at least double in value if interest at 4.2\% p.a. is compounded quarterly?
Aaron borrows \$15\,000 to buy a car. He is charged 6.8\% reducible interest compounded monthly. He wishes to pay off the loan in 3 years.
Complete the given table, leaving out the unknown variable.
Hence, use the financial solver on a CAS calculator or other technology to find the minimum value of his monthly repayments.
| Value | |
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| CpY |
Mr and Mrs Gwen held a mortgage for 25 years. Over that time, they made monthly repayments of \$4500 and were charge a fixed interest rate of 4.4\% per annum, compounded monthly.
Complete the given table, leaving out the unknown variable.
Hence, use the financial solver on a CAS calculator or other technology to determine how much Mr. and Mrs. Gwen initially borrowed.
| Value | |
|---|---|
| N | |
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| CpY |
Derek borrows \$50\,000 at a rate of 9\% (per annum) reducible interest compounded quarterly. At the end of each quarter, he makes a repayment of \$1800.
Complete the given table, leaving out the unknown variable.
Hence, use the financial solver on a CAS calculator or other technology to find how many quarters it will take for the loan to be repaid.
| Value | |
|---|---|
| N | |
| I\% | |
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| FV | |
| PpY | |
| CpY |
Xanthe borrows \$32\,000 at a rate of 6.5\% (per annum) reducible interest compounded monthly. At the end of each month she makes a repayment of \$380
Complete the given table, leaving out the unknown variable.
Hence, use the financial solver on a CAS calculator or other technology to determine how many months it will take for the loan to be repaid.
Calculate the total amount Xanthe paid.
Calculate how much Xanthe paid in interest.
| Value | |
|---|---|
| N | |
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| CpY |
Tara borrows \$15\,000 and is charged quarterly reducible interest at a rate of 7\% per annum compounded quarterly. She wishes to pay off the loan in 7 years.
Complete the given table, leaving out the unknown variable.
Hence, use the financial solver on a CAS calculator or other technology to determine the minimum value of her quarterly repayments.
Calculate the total amount Tara paid.
Calculate how much Tara paid in interest.
| Value | |
|---|---|
| N | |
| I\% | |
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| FV | |
| PpY | |
| CpY |
Tom has a mortgage of \$500\,000 reducible monthly with an annual interest rate of \\4.2\%. He makes fortnightly repayments of \$1500. Assume for this question that there are 26 fortnights in a year.
Complete the given table, leaving out the unknown variable.
Hence state the number of full years it will take to pay off the loan.
If Tom would like to pay off his loan in 10 years, what new value of N should be used?
If Tom would like to pay off his loan in 10 years, find the fortnightly repayment he needs to make, to the nearest dollar.
| Value | |
|---|---|
| N | |
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| CpY |
Pauline and Brad borrow \$330\,000 for a house extension. The bank offers them 2.75\% p.a compounded daily. They also make a payment of \$67 per day. Assume there are 365 days in a year.
Complete the given table.
Determine the whole number of years it will take until Pauline and Brad pay back the \$330\,000 loan required for the extension.
If they change their payment to \$75 per day, how many whole years will it take until they pay the loan?
How many years do they save by increasing their payment to \$75?
| Value | |
|---|---|
| N | - |
| I\% | |
| PV | |
| Pmt | |
| FV | |
| P/Y | |
| C/Y |
Caitlin borrows \$250\,000 to buy a unit and wants to pay it back in 10 years. The current interest rate is 3.2\% p.a. compounded monthly. She wishes to find the monthly payment needed to reach her goal.
Complete the given table.
Determine the monthly payment required for Caitlin to repay the \$250\,000 loan in 10 years.
How much does she pay in total over the term of the loan?
If she extends the term of the loan to 25 years, how much will her monthly payment be?
How much does she pay in total over the 25 years?
Hence, determine how much money she saves if she pays the loan back after 10 years instead of 25 years.
| Value | |
|---|---|
| N | |
| I\% | |
| PV | |
| Pmt | - |
| FV | |
| P/Y | |
| C/Y |
Pauline and Jenny take out a loan of \$120\,000 for a new caravan. The loan rate is 3.015\% p.a. compounded weekly. They decide to make payments of \$100 per week. Assume there are 52 weeks in a year.
Complete the given table.
Determine the whole number of weeks it will take until Pauline and Jenny pay back the \$120\,000 loan they borrowed for the caravan.
Assuming all payments are equal in size, how much do Pauline and Jenny pay for the caravan?
If they decide to triple their payment to \$300 per week, how many whole weeks will it take them until they pay the loan?
Hence, calculate how much money they save if they triple their payment.
| Value | |
|---|---|
| N | - |
| I\% | |
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| FV | |
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| C/Y |
A student borrows \$60\,000 to pay their student loan. The bank offers a reducing balance loan and charges a student rate of 0.95\% p.a. compounded weekly. She wants to pay the loan off completely in 8 years in equal monthly payments. Assume there are 52 weeks in a year.
Complete the given table.
State the monthly payment required.
How much should she pay each month if she wants to pay the loan off in half the time?
| Value | |
|---|---|
| N | |
| I\% | |
| PV | |
| Pmt | - |
| FV | |
| P/Y | |
| C/Y |
A young couple wish to borrow \$210\,000.
Bank 1 is advertising a reducing balance loan with an interest rate of 3.05\% p.a. compounded monthly and quarterly payments of \$5000.
Bank 2 offers them the deal that they can pay the loan in 60 installments of \$4500.
Complete the given table for Bank 1.
Calculate the number of whole quarters it takes until the loan is paid using Bank 1.
Calculate the total amount paid to Bank 2 over the duration of the loan.
Which bank should the couple choose? Explain your answer.
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| N | - |
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Stephen borrows \$12\,500 to buy a car. The bank offers a reducing balance loan with interest rate of 4.6\% p.a. compounded monthly. Stephen chooses to make weekly payments of \$100 in order to pay off the loan. Assume there are 52 weeks in a year.
What is the balance of the loan after 20 weeks?
How long does it take him to pay off the loan in years? Round your answers to two decimal places.
Kate borrows \$14\,800 to buy a car. The bank offers a reducing balance loan with an interest rate of 3.5\% p.a. compounded monthly. Kate chooses to make weekly payments of \$90 in order to pay off the loan.
What is the balance after 52 weeks?
Approximate how long it takes her to pay off the loan in years. Round your answers to two decimal places.
Valerie borrows \$345\,000 to buy an apartment. The bank offers a reducing balance loan with an interest rate of 2.35\% p.a. compounded monthly. Valerie chooses to make fortnightly payments of \$1250 in order to pay off the loan. Use a financial application on a calculator or other technology to answer the following questions. Assume there are 26 fortnights in a year.
What is the balance after 100 weeks?
Approximate how long will it take her to pay off the loan in years? Round your answers to two decimal places.
Stephen borrows \$12\,500 to buy a car. The bank offers a reducing balance loan with interest rate of 4.6\% p.a. compounded monthly. Stephen chooses to make weekly payments of \$100 in order to pay off the loan. Assume there are 52 weeks in a year.
What is the balance of the loan after 20 weeks?
How long does it take him to pay off the loan in years? Round your answers to two decimal places.