Question

You want to receive $475 at the end of each year for 4 years. Interest is 11.7% compounded annually. How much would you have to deposit at the beginning of the 4-year period?

Answer 1

To calculate the deposit required to receive $475 annually for 4 years at an 11.7% interest rate, you use the present value of an annuity formula. This requires determining the present value factor with the given rate and time, then multiplying by the annual payment.

Step-by-step explanation:

To determine how much you would need to deposit at the beginning of the 4-year period to receive $475 at the end of each year for 4 years at an interest rate of 11.7% compounded annually, you use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:
PV = Present Value of the annuity
PMT = Annual payment ($475)
r = Annual interest rate (11.7% or 0.117 as a decimal)
n = Number of periods (4 years)

First, calculate the present value factor:

= [(1 - (1 + 0.117)^-4) / 0.117]

Then, multiply the PMT by the present value factor to determine the amount needed to be deposited:

PV = $475 * Present Value Factor

Calculate and find the total present value, which is the initial deposit required.

This formula accounts for compound interest, which, as noted, can make a significant difference with larger sums of money and over longer time periods compared to simple interest.