You are born and your parents decide to invest $40 per month into a RESP at a rate of 2.7% interest compounded monthly until you're 18. Calculate the amount of money you will have when you graduate HS

Question

You are born and your parents decide to invest $40 per month into a RESP at a rate of 2.7% interest compounded monthly until you're 18. Calculate the amount of money you will have when you graduate High School

Answer 1

This is a future value annuity with no initial investment where the formula is as follows:

Annuity future value formula

C*[(1+r)^t-1]/r

,where C is the amount invested per period for t periods and the interest rate is r.

We must determine all the values in order to use the formula.

Fortunately C is given, so we know C = $40.

Next we determine t. Note, the word problem states that the annuity is paid from birth until 18 years of age, every month. This indicates that t = 18*12 = 216, since there 12 months in a year.

Next, we determine r. Again note, the word problem states that the annuity payments are compounded monthly. This means that the monthly compounding interest rate is r = 0.027/12 = 0.00225, since there are 12 months in a year.

Now, we put the values in the formula.

C*[(1+r)^t-1]/r = 40*[(1+(.027/12))^(12*18)-1]/(.027/12)

= 40*[(1+0.00225)²¹⁶-1]/(0.00225)

= 40*[0.6249/0.00225]

= 40*277.74

= 11,109.56

So, the amount after graduating high school will be $11,109.56 which will be helpful with tuition.