Question

Jose invests $4000 in an investment account paying 8% annually for 12 years. Suppose the interest was compounded quarterly instead of annually.

How much would the future value of the investment increase?

Enter your answer as a dollar amount, such as: $302.26

Answer 1

$275.6

Explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

In this question:

`P = 4000, r = 0.08, t = 12`

Anually:

`n = 1`

Then

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

`A(12) = 4000(1 + (0.08)/(1))^(12)`

`A(12) = 10072.68`

Quarterly:

`n = 4`

Then

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

`A(12) = 4000(1 + (0.08)/(2))^(12*4)`

`A(12) = 10348.28`

How much would the future value of the investment increase?

10348.28 - 10072.68 = 275.6

The future value of the investment would increase by $275.6.