Solve the problem.
-A deposit of $8000 is made in an account that earns 5.2% interest compounded quarterly. The balance in the account after n quarters is given by the sequence an = 8000(1 + 0.0524 )n, n = 1, 2, 3, ... Find the balance in the account after six years by computing a24
A) $8180.46
B) $10,907.29
C) $6946.46
D) $8644.63

Question

Quizplus · Accepted Answer

The correct formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Given that the interest rate is 5.2% or 0.052 when expressed as a decimal, compounded quarterly ($n = 4$), for 6 years ($t = 6$), the formula becomes $A = 8000(1 + \frac{0.052}{4})^{4*6}$. The given sequence formula seems to have a typo in the interest rate (0.0524 instead of 0.052), but following the correct compounding formula, calculating $A = 8000(1 + \frac{0.052}{4})^{24}$ gives the balance after 6 years, which matches closest to option B, $10,907.29, when calculated correctly.

Solve the Problem. -A Deposit of $8000 Is Made in an Account That