1. Lehlohonolo opens a savings account that bears 15% simple interest per annum. If he deposits R 5 700 how much money will he have after 11 years and 7months?
2. How long would it take for R8 400 to grow to R15 000 at a simple interest rate of 7.5% p.a.? Give your answer correct to the nearest month.
3. How much should be invested now at 8% simple interest per annum to accumulate to R12 000 in 6 years?
4. A car worth R145 000 depreciates at the rate of 16% annually according to the straight line method. What will the value of the car be after 4.5 years?
5. How long would it take for the car in the previous question to depreciate in value to R100 000? Give your answer correct to the nearest month.
6. If Sipho buys a camera for R899 at the beginning of the year 2010 and intends to sell it for R350 at the end of 2014, what would the rate of depreciation be assuming simple interest decay?
Compound Interest
7. Kwena opts for an investment with an interest rate of 8% per annum compounded quarterly. How much will he have after 6 years if he invests R2000?
8. Juju invests R18 000 into a savings account with an interest rate of 9% per annum compounded monthly. If he invests a further R10 000 into the account after 4 years, how much will he have after 6 years and 8 months?
9. How much should be invested now at 8% interest per annum compounded annually to accumulate to R12 000 in 6 years?
10. What is the annual interest rate if R8 700 is compounded semi‐annually and grows to R12 500 after 4 years?
11. A car worth R145 000 depreciates at a compound rate of 16% per annum. Calculate the book value of the car after 4,5 years.
12. A car dealer uses the straight‐line method to calculate a car’s value. The car was originally bought for R150 000. The car dealer calculates the car to be worth R85 667.89 as it is now 5 years old.
a) What rate of depreciation has the dealer used?
b) What rate of depreciation would have to be used to give the same value using the reducing balance method?
Preparation for the Mathematics examination brought to you by Kagiso Trust
Converting nominal to effective interest rate
13. Calculate the effective interest rate, if the nominal interest rate is 12.5% compounded monthly.
14. Calculate the effective interest rate, if the nominal interest rate is 12.5% compounded quarterly.
15. Calculate the effective interest rate, if the nominal interest rate is 12.5% compounded biannually.
16. Given an effective rate of 11.65%, what would the annual nominal rate compounded monthly be?
Comparing two investments
17. You are offered two savings schemes. Bank A will pay you 12% compounded monthly, and Bank B 12.5% compounded quarterly. Which is the better investment? (Hint: compare their effective rates.)
Future value of an ordinary annuity
18. What will the value of an annuity be after 30 years if R500 is deposited each year into an investment earning 6.75% per annum compounded monthly?
Sinking fund
19. You reckon that in 4 years’ time you will need to replace your car at a cost of R300 000. What fixed monthly savings must you make into an account paying 6% p.a. compounded monthly?
Present value of an annuity
20. What is the present value of an annuity that offers to pay R1000 per month for 10 years if the interest is 7% per annum compounded monthly?
Ammortisation
21. You take out a bond worth R500 000 in order to buy a house. The terms of the bond are that you pay equal monthly instalments over a period of 20 years. The interest on the bond is 9.5% per annum compounded monthly. What will your monthly repayments be?
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