Question

If $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years?

$145.23
$358.69
$613.04
$618.41

Answer 1

$613.04

Explanation:

Compound Interest Formula:

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

n = number of compounds

t = time

r = interest rate

P = principle amount (original amount)

A = final amount

Since it's compounded quarterly, that means there will be 4 compounds per year, so n=4. The interest rate has to be converted to the decimal value, and this is done by simply dividing it by 100 to get r=0.06.

Plug Values into equation:

`A = 300(1+(0.06)/(4))^(12*4)`

Simplify inside parenthesis

`A = 300(1.015)^(48)`

Calculate exponent

`A \approx 300(2.043478)`

Multiply values

`A \approx 613.04348`

Round

`A = 613.04`