Salem plans to deposit $2200 every 6 months for 15 years to save for his son's higher education. The rate of return will be 4% compounded semi-annually for the first 5 years and 8% compounded semi-annually for the subsequent 10 years. Calculate the future value of this simple annuity, if he stops payment after 5 years.

Question

Quizplus · Accepted Answer

To calculate the future value of this annuity, we first find the future value of the payments made in the first 5 years at the 4% interest rate, compounded semi-annually. Since payments stop after 5 years, we then calculate how this amount grows over the next 10 years at the 8% interest rate, also compounded semi-annually.For the first 5 years:- Interest rate per period (semi-annually) = 4% / 2 = 2%- Number of periods = 5 years * 2 = 10 periods- Payment per period = $2200Using the future value of an annuity formula: FV = P * [((1 + r)^n - 1) / r]Where P = payment per period, r = interest rate per period, and n = number of periods.FV for the first 5 years = 2200 * [((1 + 0.02)^10 - 1) / 0.02] ≈ $24,525.62For the next 10 years, this amount grows at 8% compounded semi-annually, but without additional payments. So, we use the future value of a single sum formula: FV = PV * (1 + r)^nWhere PV = present value (the amount after the first 5 years), r = interest rate per period, and n = number of periods.- Interest rate per period (semi-annually) = 8% / 2 = 4%- Number of periods = 10 years * 2 = 20 periodsFV for the next 10 years = 24,525.62 * (1 + 0.04)^20 ≈ $52,782.81Therefore, the correct answer is B) $52,782.81.

Salem Plans to Deposit $2200 Every 6 Months for 15