Question #207598

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)

Expert's answer

"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)}\\\\\nA = 2,000.00(1 + 0.12)^4\\\\\nA = \\$3,147.04\\\\\nI=3147.04-2000=\\$1147.04"

(b)

"A = 2,000.00(1 + 0.11\/4)^{4\u00d74}\\\\\nA = 2,000.00(1 + 0.0275)^{16}\\\\\nA =\\$3,087.02\\\\\nI=3087.02-2000=1087.02"

(C)

"A = 2,000.00(1 + 0.1\/12)^{12\u00d74}\\\\\nA = 2,000.00(1 + 0.008333333)^{48}\\\\\nA = \\$2,978.71\\\\\nI=2978.71-2000=\\$978.71"

(d)

"A = 2,000.00(1 + 0.0985\/365){365\u00d74}\\\\\nA = 2,000.00(1 + 0.000269863)^{1460}\\\\\nA = \\$2,965.64\\\\\nI=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.

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