Solve the problem.
-Austin invested $12,000 in an account at 8% compounded quarterly. Find the amount in Austin's account after a period of 4 years.
A)$16,150.42
B)$16,473.43
C)$4473.43
D)$16,325.87

Question

Quizplus · Accepted Answer

First, we need to determine the number of compounding periods in 4 years, since interest is compounded quarterly. There are 16 quarters in 4 years (4 quarters per year).

Next, we can use the formula for compound interest:

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

where: 
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

Plugging in the values we have:

A = 12,000(1 + 0.08/4)^(4*16)
A = $16,473.43

Therefore, the amount in Austin's account after 4 years is $16,473.43. Option B is the correct answer. We use the formula $A=P\left(1+\frac{r}{n}\right)^{nt}$, where:
- A is the final amount
- P is the principal (initial amount)
- r is the annual interest rate (as a decimal)
- n is the number of compounding periods per year
- t is the time (in years) the money is invested
Substituting the given values, we get:
$A=12000\left(1+\frac{0.08}{4}\right)^{(4)(4)}\approx\boxed{16473.43}$ (rounded to two decimal places)

Solve the Problem. -Austin Invested $12,000 in an Account at 8% Compounded Quarterly