Question

Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years?

$1,671.74
$17,028.75
$1,710.61
$8,140.92

Answer 1

A = Pe^rn = 500e^(0.082 x 15) = 500e^1.23 = $1,710.61

Answer 2

You will have $1710.61 after 15 years.

Explanation:

We know that, in case of continuous compounding,

`A=Pe^(rt)`

where,

A = Future amount

P = Principal = $500

r = rate of interest = 8.2% = 0.082

t = time period = 15 years

Putting all the values,

`A=500e^(0.082* 15)`

`=500e^(1.23)`

`=\$1,710.61`