Financial Maths - Present values.
Test Yourself 1.
To answer these questions, you will need to use the relationship involving compound interest of:
Future value = Present value × (1 + rate%)no. of periods
Present value requiring compound interest calculations. | ||||||||||||||||||||||||||||||||||||
1. Samantha wishes to make an investment now so that in 5 years time, she can receive $20,000. She knows a reliable fund which pays 7% p.a. interest payable at the end of each year.
Answer.$14,259.72 - say $14,260. |
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2. The future value of an annuity is $150,000 when the investment is over 8 years and the interest rate is 4.8% compounded monthly.
Answer.$102,248. |
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3. What single amount of money (to the nearest $10) would need to be invested today at 5.4% p.a. compounded monthly if, after 3 years, the account had a balance of $10,000?
Answer.$8,510. |
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4. Anne wishes to buy Government Bonds which will mature in 10 years time. At that time, she will receive $27,000. The rate at which she will make the investment is currently compounding at 1.7% p.a.
What is the present value of such an investment |
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Annuity-type questions using Present Value tables. | ||||||||||||||||||||||||||||||||||||
Present value | 5. An annuity paid $500 each half year for 8 years. The interest rate was 1.6% p.a.
Answer.Deposit: $7,481. |
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6. $3,000 was withdrawn from a trust account at the end of each year for 6 years. The account paid 2% p.a. interest.
Answer.Deposit: $16,804. |
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8. How much can Will borrow (nearest $) if he is prepared to repay $250 per month for 3 years? His loan will have a compound interest rate of 12% p.a. Answer.Deposit: $7,527. |
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Payment amount. | 10. The table below shows present value factors for a number of periods by monthly interest rate.
Use this table to calculate the monthly repayment required for a loan of $15,000 at 6% p.a. which is repayable over 5 years. Answer.M = 15000 ÷ 51.72556= $289.99. |
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11. David wishes to buy new car. To cover the balance of his outlay (after a trade-in) he needs to take out a loan for $20,000 over 4 years at 3.6% p.a. interest.
Answer.$448 per month. |
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12. Paula wants to go on a short holiday (in Australia of course) with some of her friends after she finishes school. She estimates she will need $1,200 for airfares, accommodation and general spending.
She thinks she can afford to repay $30 per week for the next 52 weeks and the bank will lend her the money at the rate of 0.1% per week. Can Paula repay the loan she wants to organise? Answer.Paula can borrow $1,519 -so she can reduce the repayment period (or increase her spending limit). |
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Comparison of future and present values. | Hailey invests in an annuity in which she pays $2,000 at the end of each year for 15 years. The interest rate she is paid for the investment is fixed at 6%. Answer.(i) Future value = $46,552. (ii) Total investment is $30,000. (iii) Present value = $19,424.52. |