Question

A series of 10 end-of-year deposits is made that begins with $5,000 at the end of year 1 and decreases at the rate of $300 per year with 12% interest.

a) What amount could be withdrawn at t = 10?
b) What uniform annual series of deposits (n = 10) would result in the same accumulated balance at the end of year 10?

Answer 1

To find the amount that could be withdrawn at t = 10, calculate the future value of the 10 deposits using the formula for the future value of an annuity.

Step-by-step explanation:

To solve this problem, we can use the formula for the future value of an annuity: FV = P * [(1 + r)^n - 1] / r, where FV is the future value, P is the periodic deposit, r is the interest rate per compounding period, and n is the number of compounding periods.

a) To find the amount that could be withdrawn at t = 10, we need to calculate the future value of the 10 deposits. The first deposit is $5,000, and it decreases by $300 each year. The interest rate is 12%. Substituting these values into the formula, we have:

FV = 5000 * [(1 + 0.12)^10 - 1] / 0.12