Financial Mathematics 3

DEPRECIATION

1. The purchase price of a car is R266 000.
If the vehicle depreciates at a rate of 15% p.a, calculate its value in 5 years on:
1.1. a straight line basis
1.2. reducing balance method.

2. The value of a packing machine is reduced to R108 000 three years after it was purchased.
What was the purchase price if the rate of depreciation is 18% p.a, calculated on a reducing balance?

3. Calculate the rate of depreciation, on a reducing balance, of a tractor purchased for R 750 000 if its scrap value, 8 years later is R130 000?

4. An automatic photo-printer is purchased for R150 000. It depreciates at 24% p.a.
Calculate its book value four years after it was purchased if depreciation is calculated on:
4.1. a straight line basis
4.2. a reducing balance method

5. Calculate the rate of depreciation using a reducing balance method, of a vehicle whose value reduced from R650 000 to R230 000 over a period of 9 years.

6. The book value of a copier is R27 000 four years after it was purchased. The rate of depreciation is 15% on a reducing balance.
Calculate the purchase price of the machine.

7. A computer is purchased for R16 000. It depreciates at 15% per annum.
7.1. Determine the book value of the computer after 3 years if depreciation is calculated according to the straight-line method.
7.2. Find the rate, according to the reducing-balance method, that would yield the same book value as in 7.1. after 3 years.

COMPOUND INTEREST ON MONTHLY AND DAILY BALANCES.

1. Calculate the value of an investment of R5000 after 5 years at an interest rate of 8 % p.a compounded:
1.1. annually
1.2. half-yearly
1.3. quarterly
1.4. monthly

2. Calculate the value of an investment of R25 000 after 7 years at an interest rate of 12 % p.a compounded:
2.1. annually
2.2. half-yearly
2.3. quarterly
2.4. monthly

3. A person invests at an interest rate of 9 % p.a compounded monthly. After 20 years it accumulates to R 860 000.
Calculate the initial amount invested.

4. A sum of money amounts to R3 745, 96 when invested for 4 years in a bank which offers an interest rate of 16% per annum compounded every three months.
Determine how much was invested.