Math 134 Tutorial 11 : Financial Maths - Simple and Compound Interest
REMEMBER: For Simple Interest: S = P (1 + i:n)
For Compound Interest: S = P (1 + i)n and the time periods for i and n must match
QUESTION 1
1
Find the future value of R15000 invested for 4 years at a simple interest rate of 7 %.
2
QUESTION 2
1
Find the future value of R15000 invested for 4 years at a nominal interest rate of 7 % compounded
2
(a) annually
(b) quarterly
(c) monthly
(d) continuously
QUESTION 3
Find the present value of R16000 due in 8 years’time if the interest rate in 12% compounded half-yearly.
QUESTION 4
How long will it take for an investment of R8000 to mature to R15000 at a nominal interest rate of 11%
compounded
(a) annually
(b) monthly?
QUESTION 5
How long will it take for R5000 to double itself at a nominal interest rate of 8% compounded
(a) annually
(b) continuously?
QUESTION 6
(a) What interest rate compounded quarterly will give a …nal value of R6000 on a loan of R4500 to be
repaid over 4 years?
(b) What is the future value of your investment if you deposit R2000 per month for 10 years into an account
earning 9% compounded monthly? (Annuity)
QUESTION 7
Find the e¤ective interest rate (correct to 3 decimal places) of
(a) 15% compounded monthly
(b) 16% compounded quarterly
(c) 12% compounded half-yearly
(d) 5% compounded daily
QUESTION 8
An investment of R10000 at an interest rate of 9% compounded quarterly was made 8 years ago. What
amount invested 4 years ago at 12% compounded anually would yield the same maturity value (…nal value)?
1
NOTE:
See also 2011 Tut 7 (Q1 to Q7) for more questions on these topics.
ANSWERS:
QUESTION 1
R19500,00
QUESTION 2
(a) R20 032,04 (i = 0; 075; n = 4)
(b) R20 191; 71
(c) R20 228; 99
0; 075
; n = 16
4
i=
i=
(d) R20 247; 88
QUESTION 3
R6289; 34
i=
0; 12
; n = 16
2
QUESTION 4
(a) 6; 023 years (i = 0; 11)
(b) 5; 741 years
i=
0; 11
12
QUESTION 5
(a) 9; 006 years (i = 0; 08)
(b) 8; 664 years (i = 0; 08)
QUESTION 6
x
(a) i = , x = 7; 257%
4
(b) S = 2000snei = R387 028; 55
i=
0; 09
; n = 120
12
QUESTION 7
(a) 16; 075%
i=
0; 15
; n = 12
12
(b) 16; 986%
i=
0; 16
; n=4
4
(c) 12; 360%
i=
0; 12
; n=2
2
(d) 5; 127%
i=
0; 05
; n = 365
365
QUESTION 8
An investment of R12 952; 51
2
0; 075
; n = 48
12