Question

You decide to start a retirement account and plan to work the next 40 years. If you make monthly payments of $100 into a mutual fund that expects to average returns of 12% over this period, then how much will you have when you retire?

Make sure to show your work--the equation you are using

Answer 1

There can be two assumptions - the amount is deposited into the retirement fund in the (1) beginning of every month, or (2) ending of every month.

Where the amount is deposited in the beginning of every month, it is called "annuity due".

Where the amount is deposited in the ending of every month, it is called "annuity ordinary".

Formula to calculate value for annuity due:

Formula to calculate value for ordinary annuity:

Here,

A = monthly payment = 100

r = interest rate per period of payment = interest rate per month = 1% or 0.01

n = number of payments = 40 * 12 = 480

Hence,

Value if payment is made in beginning of every month:

= 1188242

Value if payment is made in end of every month

= 1176477

If nothing is mentioned, it can be generally assumed that payment is made at end of every month.