Help me with this question

Question

Darcy began making monthly contributing to his RRSP at the age of 24. His average monthly contribution, starting 1 month after his 24th birthday, was $125 and his RRSP earned interest at an average rate of 7.5% compounded monthly. Darcy stopped making contributions when he retired at the age of 50 and started to withdraw a pension from his RRSP.

A) Determine the amount in Darcy’s RRSP on his 50th birthday.

B) Darcy decides to re-invest the total amount of his RRSP to provide an annuity for his monthly income during his retirement. Suppose Darcy was able to obtain the same average interest rate and chose a 20 year term for his annuity. What monthly pension could he withdraw for the next 20 years?

Answer 1

Monthly investments: If you make regular deposits to your account at the end of each month instead of a single lump-sum deposit, you need to modify your calculation or your spreadsheet formula.

If you deposit $100 per month for the next five years, starting from zero, you could use:

Interest on a series of investments:

=FV(0.004167,60,100)

Note that you use a monthly interest rate, and you adjust the number of periods to 60 months.

To calculate by hand, use the future value of an annuity calculation:

Example of a series of investments:

1. FV = Pmt x (((1 + r) ^ n) – 1)/r)
2. FV = 100 x (((1 + 0.004167) ^ 60) – 1) / 0.004167)
3. FV = 100 x (1.283 – 1) / 0.004167
4. FV = 100 x 68.0067
5. FV = 6800.67