You save $53 per month for 21 years in a savings account earning 2% interest compounded monthly. The total amount in the account after 21 years will be $$53 \left[ \left( 1 + \frac { 0.02 } { 12 } \right) ^ { 252 } - 1 \right] \left( 1 + \frac { 12 } { 0.02 } \right)$$ . How much money is in the account after 21 years? Round your answer to two decimal places.
A)$48,462.10
B)$13,641.56
C)$16,609.10
D)$14,867.44
E)$34,698.81

Question

Quizplus · Accepted Answer

The formula given is a variation of the future value of a series formula in finance, specifically for calculating the future value of an annuity with regular deposits. The calculation is based on the formula for the future value of an annuity due to compound interest. Plugging the values into the formula:$$53 \left[ \left( 1 + \frac { 0.02 } { 12 } \right) ^ { 252 } - 1 \right] \left( \frac { 12 } { 0.02 } \right)$$Given that there are 21 years and the interest is compounded monthly, the total number of periods (n) is $21 \times 12 = 252$. The monthly interest rate (r) is $\frac{0.02}{12}$.The calculation will yield the total amount in the account after 21 years, which, when calculated correctly, results in approximately $16,609.10, making option C the correct answer.

You Save $53 Per Month for 21 Years in a Savings