Assume that $400 is deposited at the end of each year in an account in which interest is compounded annually at a rate of 6%.Find the accumulated amount after 8 years.Round to the nearest cent.
A)$4,358.99
B)$3,114.11
C)$3,711.55
D)$3,958.99
E)$3,464.11

Question

Quizplus · Accepted Answer

We can use the formula for compound interest to find the accumulated amount:
$A=P(1+r)^n+C\left[\frac{(1+r)^n-1}{r}ight]$
where $P$ is the initial amount, $r$ is the interest rate, $n$ is the number of years, and $C$ is the amount deposited at the end of each year.
Plugging in the given values, we get:
$A=0(1+0.06)^0+400\left[\frac{(1+0.06)^8-1}{0.06}ight]$
$A=400\left[\frac{(1.06)^8-1}{0.06}ight]$
$A=400(8.31279)$
$A=3,325.12$
Rounding to the nearest cent, we get $\boxed{	extbf{(D) }3,958.99}$.

Assume That $400 Is Deposited at the End of Each