Final answer:
To calculate the initial deposit needed to achieve a future value of $60,000 with an annual interest rate of 8.6% compounded quarterly over 15 years, use the compound interest formula and solve for the principal P.
Step-by-step explanation:
The student is asking about the initial deposit required to reach a future value through the power of compound interest. To find out how much money should be deposited in a bank account paying 8.6% interest, compounded quarterly, to reach a future value of $60,000 over 15 years, we use the compound interest formula:
A = P(1 + r/n)nt
Where:
- A is the future value of the investment/loan, including interest.
- P is the principal investment amount (initial deposit).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years that the money is invested for.
We can rearrange the formula to solve for the principal P:
P = A / (1 + r/n)nt
Substituting the given values:
P = $60,000 / (1 + 0.086/4)4*15
After calculating P, we will find out the amount of money that should be initially deposited to achieve the desired future value after 15 years.