Question

If $10,000 is invested at 2 percent semi-annually for 5 years, what is the amount at the end of the

term?

Answer 1

The amount at the end of the term is $ 11046

Solution:

The formula for compound interest, including principal sum, is:

`A = p(1+(r)/(n))^(nt)`

Where,

A = the future value of the investment including interest

P = the principal investment amount

r = the annual interest rate in decimal

n = the number of times that interest is compounded per unit t

t = the time the money is invested

From given,

p = 10000

t = 2 years

`r = 2 \% = (2)/(100) = 0.02`

n = 2 ( since interest is compounded semiannually)

Substituting the values in formula,

`A = 10000(1+(0.02)/(2))^(2 * 5)\\\\A = 10000(1+0.01)^(10)\\\\A = 10000(1.01)^(10)\\\\A = 10000 * 1.104622\\\\A = 11046.2212 \approx 11046`

Thus the amount at the end of the term is $ 11046