Question

Thirteen years ago, Mr. Lawton rolled a $18,000 retiring allowance into an RRSP that subsequently earned 10.1% compounded semiannually. Four years ago he transferred the funds to an RRIF. Since then, he has been withdrawing $1100 at the end of each quarter. If the RRIF earns 8.1% compounded quarterly, how much longer can the withdrawals continue? (Do not round intermediate calculations and round up the number of payments, n, to the next whole number.)

Answer 1

The question involves compound interest and annuity calculations to determine the duration of funds in an RRIF based on certain withdrawal rates and interest rates. Formulas for future value of investments and present value of annuities are used to find the solution.

Step-by-step explanation:

The student's question involves calculating the future value of a Registered Retirement Savings Plan (RRSP) that has been rolled over into a Registered Retirement Income Fund (RRIF) and determining how long the funds can last given a series of withdrawals and an annual interest rate. Using the annuity formula, we can calculate the amount of money Mr. Lawton had in his RRSP before transferring it to an RRIF, and then use the annuity formula again to determine how many quarterly withdrawals of $1100 Mr. Lawton can make from his RRIF at an 8.1% annual rate compounded quarterly.

First, we need to calculate how much the $18,000 RRSP grew over 13 years at a 10.1% annual rate compounded semiannually. Then we will determine the future value of the RRIF after 9 years (the 4 years of growth followed by 5 years of withdrawals) and the present value of the remaining annuity payments (quarterly withdrawals) to solve for the number of periods (n).