Final answer:
The student needs to use the compound interest formula to calculate the present value required to achieve a future amount of $25,700 in 8 years at an 8% interest rate compounded semiannually. By rearranging the formula, P = A / (1 + r/n)^nt, and substituting the given values, the student can find out how much they need to deposit now.
Step-by-step explanation:
To determine the amount a medical student must deposit now to have $25,700.00 in 8 years at an 8% interest rate compounded semiannually, the formula for compound interest must be used:
The compound interest formula is P = A / (1 + r/n)nt,
where:
- P is the principal amount (the initial amount of money)
- A is the future value of the investment/loan, including interest
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per year
- t is the time the money is invested/borrowed for, in years
In this case:
- A = $25,700
- r = 8% or 0.08
- n = 2 (since the interest is compounded twice per year)
- t = 8 years
To find the present value (P), we must rearrange the formula:
P = $25,700 / (1 + 0.08/2)2*8
Calculating this gives us the principal amount that needs to be deposited now.
Remember, it is critical to convert the interest rate to a decimal and to use the exact number of compounding periods per year in your calculations to get the correct present value.