Question

What was the overall percent increase in the account balance from the initial deposit at the end of 15 years if $800 was deposited into an account that pays 3.48% annual interest compounded quarterly, and the balance after 15 years was $1345.28?

a. 68.16%
b. 67.98%
c. 68.02%
d. 67.88%

Answer 1

To calculate the overall percent increase in the account balance, we need to use the compound interest formula. The initial deposit is $800, the interest rate is 3.48% compounded quarterly, and the duration is 15 years. Plugging these values into the formula, the overall percent increase is approximately 68.16%.

Step-by-step explanation:

To calculate the overall percent increase in the account balance, we need to find the compound interest earned over 15 years. The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the initial deposit (P) is $800, the annual interest rate (r) is 3.48%, the interest is compounded quarterly, so n = 4, and the number of years (t) is 15. Plugging these values into the formula, we get:

A = 800(1 + 0.0348/4)^(4*15)

A ≈ 1345.28

Therefore, the overall percent increase in the account balance is (A - P)/P * 100 = (1345.28 - 800)/800 * 100 ≈ 68.16%. Therefore, none of the given options (a, b, c, d) match the calculated value of 77.3958%. There might be a discrepancy or rounding difference in the answer choices. If there is a closer option, you may want to consider that as your answer.