Question

suppose you contribute $2500 to an RRSP at the beginning of every six months for 25 years, and then use the accumulated funds to purchase an annuity paying $2500 at the beginning of each month. how long after the start of the annuity will the last payment be made? Assume that the RRSP earn 8% compounded semiannually and the funds invested in the annuity earn 5.1% compounded monthly.(use formula)

Answer 1

The last payment will be made approximately 15 months (or 1 year and 3 months) after the start of the annuity.

Step-by-step explanation:

To solve this problem, we need to calculate the future value of the contributions made to the RRSP for 25 years and then calculate the time it will take for the accumulated funds to be depleted by the annuity payments.

Step 1: Calculate the future value of the contributions made to the RRSP:

Using the compound interest formula, FV = PV * (1 + r/n)^(nt), where PV is the present value (contribution), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, PV = $2500, r = 8% (compounded semiannually, so n = 2), and t = 25 years. Plugging in the values, we get:

FV = $2500 * (1 + 0.08/2)^(2*25) = $2500 * (1 + 0.04)^50 = $2500 * (1.04)^50 ≈ $9,619.19

Step 2: Calculate the time it will take for the accumulated funds to be depleted by the annuity payments:

Using the annuity formula, n = log((PMT / (r/n)) + 1) / log(1 + (r/n)), where PMT is the annuity payment, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, PMT = $2500, r = 5.1% (compounded monthly, so n = 12), and FV = $9,619.19. Plugging in the values, we get:

n = log(($2500 / (0.051/12)) + 1) / log(1 + (0.051/12)) ≈ 14.8277