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Theory of Interest Tutorial 1-5, Summary and lecture notes
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Summary of tutorial 1-5, with additional notes and lecture notes.
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Tutorial 1
1) Percy can invest R17600. He should invest his money for
a) three years at a simple rate of interest of 10% p.a. or three years at a compound interest rate of 9% p.a.?
b) eight and a half years at a simple rate of interest of 10% p.a. or eight and a half years at a compound interest
rate of 9% p.a.?
2) Sarah borrowed RK on 1 July 2019 from her brother at a simple interest rate. She had to repay either R11745.38
after 8 months or R12768 after 16 months.
a) Find the amount of interest (in total) added during the last 8 months.
b) How much interest had to be paid per month?
c) Calculate
i) the total interest for the first 8 months,
ii) K,
iii) and the simple interest rate i per annum.
d) How many months after 1 July 2019 would the total debt be at least R15000?
3) Conrad has R3700 to invest. The rate of interest is 15% p.a.
a) Find the accumulated amount after 8 years.
b) After how many years (to 2 decimals) will the accumulated amount be equal to R7000?
c) What amount should he invest (instead of R3700) to have an accumulated amount of R7000 after exactly 4
years?
d) At which annual interest rate will the R3700 accumulate to R7000 in 5 years’ time?
4) Conrad (of question 3) invested R6825.15 at 14.5% p.a. compounded monthly.
a) Find the accumulated value after
i) 5 years,
ii) 7 years.
b) At the end of the 5th year the rate of interest is reduced to 13% p.a. compounded monthly. What is the
accumulated amount at the end of the 6th year?
c) How many months after the first 6 years will the accumulated amount exceed R17000 for the first time?
d) How many months is needed in (a) for the R6825.15 to double itself?
5) Currently Jean has R10450 in a bank account which earns interest at i(4) = 0.17 p.u.p.a.
a) How much can he withdraw today if he wants R12000 in the account in two years’ time?
b) What amount can he withdraw in exactly 12 months if he wants R10000 in the account three years from today?
6) Jake invested R12500 on 1 January 2014 with a bank where interest was compounded at 14% p.a. quarterly until
1 July 2017 when the rate was changed to 12% p.a. compounded monthly.
a) What was the amount in the account on 1 July 2017?
b) What was the amount in the account on 1 October 2019?
c) How much interest did Jake earn during 2018?
d) Suppose Jake withdrew R15000 on 1 July 2018. What would the amount in the account be on 1 October 2019
and how many months after 1 October 2019 would he be able to withdraw as much as R15000 again?
e) How much could Jake withdraw on 1 July 2018 (instead of the R15000) so that there will be exactly R12000 in
the account on 1 October 2019?
7) Sharon bought a Persian carpet for R18000 and sold it 5 years later for R36190. At what interest rate
a) per annum and
b) per annum compounded monthly,
did her investment grow in the 5 years?
Tutorial 1 of 11
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