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

Answer:

$275.6

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

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

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(12) = 4000(1 + \frac{0.08}{1})^{12}$

$A(12) = 10072.68$

Quarterly:

$n = 4$

Then

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(12) = 4000(1 + \frac{0.08}{2})^{12*4}$

$A(12) = 10348.28$

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.