Question

Suppose you start saving for retirement by depositing $4,000 EVERY YEAR into your retirement account. If your annual return is 8%, how much will you have in 45 years? How much would you have if all deposits were made on the FIRST of the year (as opposed to the last day of the year)?

Answer 1

First we need to Calculate amount accumulated after 45 years (if deposits are made on last day of year)

Amount deposited per year = $4000, Annual return = 8%, No of years = 45

These end of the year deposits form an ordinary annuity We can calculate amount after 45 years by finding of the future value of ordinary annuity by using FV function in excel.

Formula to be used in excel: =FV(rate,nper,-pmt,pv,type)

In the formula pv = 0 as there is no initial lumpsum deposit and type = 0 as deposits are made at end of year.

Using FV function in excel, we get future value or amount accumulated after 45 years = $1546022.47

Hence Amount accumulated after 45 years(assuming last day of year deposits) = $1546022.47

Now we will calculate the amount accumulated after 45 years (if deposits are made on first day of year)

Amount deposited per year = $4000, Annual return = 8%, No of years = 45

These beginning of the year deposits form an annuity due We can calculate amount after 45 years by finding of the future value of annuity due by using FV function in excel.

Formula to be used in excel: =FV(rate,nper,-pmt,pv,type)

In the formula pv = 0 as there is no initial lumpsum deposit and type = 1 as deposits are made at beginning of year

Using FV function in excel, we get future value or amount accumulated after 45 years = $1669704.27

Hence Amount accumulated after 45 years(assuming first day of year deposits) = $1669704.27