Final answer:
To calculate the total amount of Rebecca's RRSP after 11 years, we separately calculate the future value of the annuity for the first 7 years at 3.90% semi-annually and the remaining 4 years at 4.50% semi-annually. We then sum the future values, accounting for the compounded interest over the 11-year period.
Step-by-step explanation:
Rebecca invested $2,200 at the beginning of every 6 months in an RRSP for 11 years. The investment scenario involves two different interest rates over two distinct periods: for the first 7 years, the interest rate was 3.90% compounded semi-annually, and for the following 4 years, it was 4.50% compounded semi-annually. To determine the total amount in her RRSP after 11 years, we need to calculate the future value of an annuity investment for each period separately and then sum them.
First, we calculate the future value of the annuity for the 7 years at 3.90% interest compounded semi-annually using the formula: FV = P * [((1 + r/n)^(nt) - 1) / (r/n)], where P is the payment per period, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Then, we'll calculate the amount that has accumulated over these 7 years, which will also earn interest for the next 4 years at the new rate of 4.50% compounded semi-annually. We'll use the future value of a lump sum formula, which is FV = PV * (1 + r/n)^(nt), where PV is the present value of the total amount from the first 7 years.
Lastly, we calculate the future value of the annuity for the remaining 4 years at the 4.50% interest rate and sum all the amounts to get the total value of the RRSP after 11 years.