Question

I am having trouble understanding what value to use for each function. The question is:

"Tom plans to save $88 a month, starting today, for 22 years. Dean plans to save $88 a month for 22 years, starting one month from today. Both Tom and Dean expect to earn an average return o 5.27 percent APR on thier savings and both will make the same number of deposits. At the end of the 22 years, how much more (in $) will Tom have than Dean?"

Answer 1

Basically both are the questions of finding Future value of annuity but one is having the first deposit made at the beginning of the year and one at the end of the year. So we need to solve keeping this in mind:

Tom will find FV using the beginning of the period formula:

• FV= Future Value
• r = APR
• R is divided by 12 as we are making monthly contributions
• P is the periodic payment
• t is the number of years and it is multiplied by 12 as monthly payments are made every year and so the number of periods is 12 times the number of years

Dean will find FV using the end of the period formula:

So the difference between Tom's and Dean's FV = $191.83

The difference between the two formulas is that the beginning of the period value is compounded one more time as compared to the end of the month value because both the values need to be compared at the end of 22 years.