Question

1. James invested 150,000.00 at 2.5% interest compounded semi-annually. Find the maturity value if he invests for (a) 4years? (b) 8years? (c) How much is the additional interest earned due to the longer time?

Answer 1

for compounded interest rate:

$P=R(1+\frac i n)^{n*t}$ , where P - current amount, R - initial amount, i - annual interest rate, n - number of payments in one year, t - number of years

a)

$P=150000(1+\frac {0.025} 2)^{2*4}\approx 165673$

b)

$P=150000(1+\frac {0.025} 2)^{2*8}\approx 182983$

c) Percent gained for 4 years: ${\frac {165673} {150000}}-1\approx0.1045=10.45$ %

Percent gained for 8 years: ${\frac {182983} {150000}}-1\approx0.2199=21.99$ %

So,  additional interest earned due to the longer time is 21.99% - 10.45% = 11.54%