Question

Janette invested $2000 at 5% compounded annually for 5 years. How much interest did she earn at the end of the 5 year period?

Answer 1

At the of the first year, she has the principal plus the interest on the principal

P1 = 2000 + 5% * 2000 = 2000(1 + 5%)

At the of the second year, she has the principal P1 plus the interest on P1

P2 = P1 + 5% * P1 = P1(1 + 5%)

Substitute P1 by 2000(1 + 5%) found above to find

P2 = 2000 * (1 + 5%) 2

Continuing with this process, it can easily be shown that a the end of the 5th year, the principal is given by

P5 = 2000 * (1 + 5%) 5

= 2000 * (1 + 0.05) = $2552.56

The interest earned at the end of 5 years is

$2552.56 - $2000 = $552.56

intereste is $552.56