Revision questions
Question 1
How long will it take a sum of money to treble itself at 14 percent?
Answer: 8.38 years
Question 2
R100 is invested at 10 percent per annum (pa) compounded semi-annually. After 3 months,
the interest rate changes to 12 percent per annum compounded monthly. Find the value of
the investment after 2 years.
Answer: R126.28
Question 3
A monthly deposit of R113 is made once a month into an account at an interest rate of 13
percent pa compounded monthly. How much is in the account immediately after the 14
monthly deposit of R113?
Answer: R1698.37
Question 4
Find the accumulated amount of R468 invested at 13 percent pa
for 3 years.
Answer: R675.28
Question 5
The interest rate for an investment is 7 percent per annum compounded monthly. Find the
effective interest rate per annum.
Answer: 7.23%
Question 6
What amount of money must be invested now so as to accumulate to R1751 in 17 months
time at 12 percent pa compound interest.
Answer: R1478.50
Question 7
If an investment amount is to double in 3 years, find the nominal interest rate at which it must
be invested if interest is compounded quarterly.
Answer: 23.79%
Question 8
Find the amount in an account after 13 monthly payments of R182 have been made if R211
was withdrawn from the account after 4 months (ie at the time of the 4th R182 payment) and
again after 11 months. (ie. at the time of the 11th R182 payment). Interest is calculated at 13
percent pa compounded monthly.
Answer: R2077.98
Question 9
A couple, who are both working, invest R160 a month each in a joint savings account which
carries interest of 20 percent pa compounded monthly. After 3 years the interest rate drops
to 13 percent and the couple continue paying into the account for a further year.
How much money will be in the account at the end of this period? Assume that no withdrawals
were made.
Answer: R21844.35
Question 10
A student loan of R6856 is to be repaid by 21 equal monthly instalments. Assuming that
instalments are due at the beginning of each month and that the first instalment is payable
immediately, what is the amount of each instalment? Interest is 15 percent pa compounded
monthly.
Answer: R368.62
Question 11
If an investment of R12510 has grown to R44986 over 4 years where interest is compounded
half yearly, what is the nominal rate of interest pa on the investment?
Answer: 34.70%
Question 12
An advertisement for a new motor car encourages you to purchase it for a deposit
of R14949 and monthly payments of R1830 at an interest rate of 13 percent pa
compounded monthly. If the repayment period is 47 months with payments in
arrears, calculate the cost price of the motor car.
Answer: R82071.58
Question 13
You recently won the lotto and can either choose between taking the lump sum of R1414424
or an annuity of R253 716 a year. The annuity is expected to pay into perpetuity. The interest
is expected to be 11 pa compounded annually. Which option will you choose?
Answer: Choose annuity
Question 14
Sikele Trading company had 864 stores in 2001 and at the end of 2011 had 640 stores. What
was the growth rate in stores over the period?
Answer: -2.96 years
Question 15
Helene invests R9735 in a savings account that pays interest at 5 percent pa compounded
monthly. Exactly 5 years later the interest rate changes from 5 to 6 percent but now it is now
compounded continuously. How much total interest will Helene have earned after 9 years?
Answer: R6147.35
Question 16
A vehicle is valued at R164265. The deposit is 15 percent and residual 20 percent. The
maturity period is 60 months and interest rate is 12 percent pa compounded monthly. What
would you expect the repayments to be on the vehicle?
Answer: R2703.62
Question 17
Your financial planner offers you two different investment plans. Plan 1 is a R3368 annual
perpetuity. Plan2 is a 11 year, R10192 annual annuity. Both plans will make their first payment
one year from today. At what discount rate would you be indifferent (ie same rate) between
these two plans? (Hint: PV’s)
Answer: 3.71%
Question 18
Mambo is 25 years old and currently earns R9262 per month. She wants to retire at age 60
and wishes to earn the equivalent amount (same buying power) which she currently enjoys.
Inflation is expected to remain at 5 percent pa until retirement. A bank is prepared to offer
Mambo 10 percent pa compounded monthly on any savings until she retires. Furthermore
Mambo believes that she can earn 7 percent pa compounded monthly once she has retired.
She expects to receive a monthly annuity once on retirement and expects to be on retirement
for 24 years. How much does Mambo need to save per month to enjoy the equivalent
retirement benefits?
Answer: R1874.79