Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

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.

How much should Samantha invest now to attain her goal (to the nearest $10)?

Answer.$14,259.72 - say $14,260.
  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.

What is the present value of the annuity?

Answer.$102,248.
  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.
  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
(to the nearest $10)?

Answer.Present value = $22,810.
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.

What was the amount deposited initially (nearest $) to provide for that annuity?

Answer.Deposit: $7,481.
  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 $3,000 was withdrawn from a trust account at the end of each year for 6 years.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.

How much was originally deposited into this account (nearest $) to enable the withdrawals?

Answer.Deposit: $16,804.
  7.
 

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.
  9.
Payment amount. 10. The table below shows present value factors for a number of periods by monthly interest rate.
Periods 0.50% 0.60% 0.70% 0.80%
55 47.98145 46.72784 45.51944 44.35439
56 48.73776 47.44318 46.19607 44.99443
57 49.49031 48.15425 46.86799 45.62940
58 50.23911 48.86109 47.53525 46.25932
59 50.98419 49.56370 48.19786 46.88425
60 51.72556 50.26213 48.85587 47.50421

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.
  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.

How much will David's monthly repayments be to pay for his new car?

Answer.$448 per month.
  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).
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%.

(i) Use the future value table to determine how much will be in her investment account at the end of 15 years.

(ii) What was Hailey's total investment?

(iii) Calculate the present value of Hailey's annuity.

(iv) Explain the difference between the answers for the previous two parts.

Answer.(i) Future value = $46,552.
(ii) Total investment is $30,000.
(iii) Present value = $19,424.52.