Question

Matano upon retirement came across the following investment regimes;

a) 12% p.a compounded annually

b) 11% p.a compounded quarterly

c) 10% p.a. compounded monthly

d) 9.85% p.a compounded continuously

 

advise

i) As a rational lender which one would you choose?                                               (3 marks)

ii) As a rational borrower which of the regimes would you choose?                         (3 marks)

 

Answer 1

$A=P(1+\frac{r}{n})^{nt}$

Interest=A-P

where A is the amount ,P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods

For example let's take P=2000, t=4years

(a)

$A = 2,000.00(1 + \frac{0.12}{1})^{(1)(4)}\\ A = 2,000.00(1 + 0.12)^4\\ A = \$3,147.04\\ I=3147.04-2000=\$1147.04$

(b)

$A = 2,000.00(1 + 0.11/4)^{4×4}\\ A = 2,000.00(1 + 0.0275)^{16}\\ A =\$3,087.02\\ I=3087.02-2000=1087.02$

(C)

$A = 2,000.00(1 + 0.1/12)^{12×4}\\ A = 2,000.00(1 + 0.008333333)^{48}\\ A = \$2,978.71\\ I=2978.71-2000=\$978.71$

(d)

$A = 2,000.00(1 + 0.0985/365){365×4}\\ A = 2,000.00(1 + 0.000269863)^{1460}\\ A = \$2,965.64\\ I=2965.64-2000=965.64$

(i)A rational lender would choose option a because it earns highest interest.

(ii)A rational borrower should choose option d because it earns low interest rate.