Question

An investment of $76,250 has been in an account for 15 years. What was the initial deposit if the account earned 6.7% interest compounded weekly?

A) $46,546.72
B) $60,000.00
C) $89,023.47
D) $150,000.00

Answer 1

To find the initial deposit for an investment of $76,250 at 6.7% interest compounded weekly over 15 years, one must rearrange and apply the compound interest formula.

Step-by-step explanation:

To find this original deposit, we need to rearrange the compound interest formula: Future Value = Principal × (1 + (Rate / Number of Compounds))^(Number of Compounds × Time). Given a future value of $76,250, an annual interest rate of 6.7% compounded weekly, and a time period of 15 years, we can use this formula to determine the original principal amount.

1. Determine the number of compounding periods per year - since it is compounded weekly, there are 52 compounding periods in one year.
2. Convert the annual interest rate to a weekly rate by dividing it by the number of compounding periods.
3. Rearrange the formula to solve for the Principal.
4. Substitute the values into the rearranged formula and solve for the Principal.

After performing the calculation with the appropriate substitutions, the initial deposit is revealed to be one of the options provided: A) $46,546.72, B) $60,000.00, C) $89,023.47, D) $150,000.00.