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

Annual 1.
 

2.
  3.
  4.
Annuity-type questions using Present Value tables.
Present value

5. Interest rate converts to 1.6% ÷ 2 = 0.8%.

Number of periods: 8 × 2 = 16 months.

PV Interest Factor (from table): 14.9623

Deposit: $500 × 14.9623 = $7,481.
  6. Interest rate does not need conversion: 2.0%.

Number of periods: 6 years.

PV Interest Factor (from table): 5.6014

Deposit: $3,000 × 5.6014 = $16,804.
  7.
  8. Interest rate converts to 12% ÷ 12 = 1.0%.

Number of periods: 3 × 12 = 36 months.

PV Interest Factor (from table): 30.1075

Deposit: $250 × 30.1075 = $7.527.
  9.
Monthly 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. Interest rate converts to 3.6% ÷ 12 = 0.3%.

Number of periods: 4 × 12 = 48 months.

PV Interest Factor (from table): 44.6419

20000 = M × 44.6419

∴ M = $448.00 per month. 
  12. Interest rate: 0.1%.

Number of periods: 52 weeks.

PV Interest Factor (from table): 50.6465

Present value = 30 × 50.6465

∴ Possible loan = $1,519.

Happy Schoolies Paula!!! 
 

13. (i) $2000 × 23.2760 = $46,552.

(ii) Investment = $2000 × 15 years = $30,000.

(iii)

(iv) As time passes, the value of money decreases due to inflation, etc. In this case due to the interest rate.

Hence although $30,000 is actually paid, the value of that amont in today's dollar is reduced to $19,424. Interpreting this result another way, we can say that we could invest a single amount now of $19,424 at 6% p.a. and receive $46,552 in 15 years.