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
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
I'm not sure when to use present value or future value. Do you have a trick to remember the difference?
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.
Thank you
To determine how long Farah will receive payments from the annuity, we need to find the number of months for which the annuity payments can be sustained with the available funds.
Let's break down the problem step by step:
Step 1: Calculate the interest earned on the funds.
To determine the interest earned annually, we can calculate:
Interest Earned Annually = Principal Amount x Interest Rate
In this case:
Principal Amount = $600,000
Interest Rate = 5% = 0.05
Interest Earned Annually = $600,000 x 0.05 = $30,000
Step 2: Determine the monthly interest rate.
Since the annuity pays monthly, we need to calculate the monthly interest rate.
Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1
In this case:
Annual Interest Rate = 5% = 0.05
Monthly Interest Rate = (1 + 0.05)^(1/12) - 1
Step 3: Calculate the number of months the annuity can sustain payments.
To find out how long Farah will receive payments, we need to calculate the number of months using the formula for the present value of an annuity:
Number of Months = log(Payment / (Payment - Principal x Monthly Interest Rate)) / log(1 + Monthly Interest Rate)
In this case:
Payment = $3,500
Principal = $600,000
Monthly Interest Rate = calculated in Step 2
Number of Months = log($3,500 / ($3,500 - $600,000 x Monthly Interest Rate)) / log(1 + Monthly Interest Rate)
By substituting the values and performing the calculations, we can determine the number of months for which Farah will receive payments from the annuity.