Farah has $600,000 in her RRSP and wishes to retire. She is thinking of using the funds to purchase an annuity that earns 5% compounded annually and pays her $3,500 at the end of each month. If she buys the annuity, for how long will she receive payments

Answer 1

The standard formulas can only be used if the compounding period and the payment period are the same.

Since they are not in your question, this makes it rather messy.
We first have to find the monthly rate equivalent to 5% compounded annually.
We can't just divide the .05 by 12.

let the monthly rate be i
then (1+i)^12 = 1.05
1+i = 1.05^(1/12) = 1.00407412..
i = .00407412...

3500(1 - 1.00407412^-n)/.00407412 = 600000
1 - 1.00407412^-n = .69842108...
.3015789... = 1.00407413^-n
using logs
log .3015789... = -n(log 1.00407413)
n = 294.82 months
or appr 24.6 years

Answer 2

I'm not sure when to use present value or future value. Do you have a trick to remember the difference?

Answer 3

The difference between present value and future value is really in the wording of the question. If the question says you want $30,000 for first year post secondary school what should you save or invest now... that is asking what is the present value of the $30,000 needed. But the future value questions are the ones that say... you start investing at the age of 16, how much will you have when you are 65. This is the future value of your money. So again... it is in the way the question is worded.

Answer 4

Thank you