A deposit of $\$$ 200 is made each month in an account that earns 8.4% interest, compounded monthly. The balance in the account after n months is given by $A _ { n } = 200 ( 201 ) \left[ ( 1.007 ) ^ { n } - 1 \right]$ . Find the balance after 22 years by computing the 264th term of the sequence. Round your answer to two decimal places.
A)$213,316.53
B)$293,716.53
C)$6,667.78
D)$86,634.61
E)$281.40

Question

Quizplus · Accepted Answer

The correct formula for the balance after n months for a monthly deposit account with monthly compounding interest is $A_n = P \left( \frac{(1 + r)^n - 1}{r} \right)$, where P is the monthly deposit and r is the monthly interest rate. Given P = $200 and an annual interest rate of 8.4%, the monthly interest rate is $0.084/12 = 0.007$. Plugging n = 264 (22 years * 12 months) into the given formula, the balance is correctly calculated as option A, $213,316.53.

A Deposit Of $\$$ 200 Is Made Each Month in an Account That Earns