Question

Bernard invests $400 in a bank account that earns 1% annual interest compounded semi-annually.

How much interest will he have earned after two years?

Answer 1

Interest earned after two years = $8.06

Explanation:

The formula for compound interest is given as:

`FV = P(1 + (r)/(n) )^(nt)`

FV = Future Value = ?,

P = Principal (the amount deposited or invested) = $400,

r = annual interest rate (in decimal) = 1% = 0.01

n = number of times the principal is compounded per year = 2 (since it is s compounded semi-annually i.e every 6 months. So in 12 months, it will be compounded twice),

t = time (in years) = 2.

So, we have

`FV = 400(1 + (0.01)/(2) )^(2(2)) = 400(1.005)^(4) \\\\ FV = 400(1.0201505006) = 408.06`

Future Value = $408.06 (i.e. after two years there will be $408.06 in Bernard's bank account)

But what we need to know is how much interest Bernard will have earned

= Future Value - Principal

= $408.06 - $400

= $8.06

NB: For the calculations on Future Value (FV), carry them out step by step using order of operations and keep as many decimals as you can until the last step. The final answer should be approximated to 2 decimal places just as I did in the preceding solution.