Question

Alicia invested $32000 into an account earning 3% annual interest compounded quarterly. She makes no other deposits and does not withdraw any money. What is the balance of Alicia's account in 7 years?

Answer 1

A = P(1+r/n)^(nt)
A = 32,000(1+0.03/4)^28
A = 39,446.78 ...........this is your answer

Answer 2

The formula for compound growth is:

$P=P_{0}(1+\frac{r}{n})^{nt}$

Where,

• P is the future value
• $P_{0}$ is the initial deposit
• r is the annual rate of interest (in decimal)
• n is the number of times compounding happens in a year (annual means n=1, compounding semi-annually means n=2, compounding quarterly means n=4 etc.)
• t is time in years

We need to solve for P. From the given information, we can write:

$P_{0}=32,000$

$r=\frac{3}{100}=0.03$

$n=4$ (since compounded quarterly)

$t=7$

Plugging in all the information in the equation, we get:

$P=32,000(1+\frac{0.03}{4})^{(4)(7)} \\P=32,000(1.0075)^{28}\\P=32,000(1.2327)\\P=39,446.4$

Alicia's account balance at end of 7 years is $39,446.4.

ANSWER: $39,446 (rounded to the nearest dollar)