Amount of an RRSP

Date: 03/24/2002 at 13:03:46
From: Veronica
Subject: Amount of an RRSP

I am having problems figuring this math problem out.  It would be 
great if you could help me.

Brian makes $2500 deposits into his Registered Retirement Savings Plan 
on his 20th, 25th, 30th, 35th, and 40th birthdays. The RRSP pays 7% 
per annum, compounded annually. Determine the value of Brian's RRSP 
when he's 65.

Thank you!

Date: 03/24/2002 at 23:33:14
From: Doctor Twe
Subject: Re: Amount of an RRSP

Hi Veronica - thanks for writing to Dr. Math.

The easiest way to figure out the total is to consider each of the 
five deposits separately. First, find the value of the first $2,500 
deposit after 45 years. Then find the value of the second $2,500 
deposit after 40 years, and so on. Sum those totals and you have the 
total value of the account.

Do you know how to find the value of a deposit after n years? The 
formula is:

     FV = PV * (1 + R/N)^(T*N)

where: FV is the future value of the investment
       PV is the present value (amount deposited)
       R is the interest rate, expressed as a decimal
       N is the number of interest periods per year
       T is the number of years

Since the interest is compounded annually, N = 1 and you can "drop" it 
from the equation. We also want to convert the interest rate from a 
percent to a decimal, so we move the decimal point 2 places to the 
left:

     R = 7% = .07

Thus, for the first $2,500 deposit we have:

     FV = PV * (1+ R)^T

        = $2,500 * (1 + .07) ^ 45

        = $2,500 * (1.07)^45

        = $2,500 * 21.00245...

        = $52,506.13

Can you finish the problem from there?

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/