Question

You plan to save $2,400 a year and earn an average rate of interest of 5.6 percent. How much more will your savings be worth at the end of 40 years if you save at the beginning of each year rather than at the end of each year

Answer 1

Answer:

If the deposits are made at the beginning of the year, the future value will increase by $18,821.1.-

Explanation:

Giving the following information:

Annual deposit= $2,400

Interest rate= 5.6%

Number of periods= 40

First, we will calculate the future value when the deposits are made at the end:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {2,400*[(1.056^40) - 1]} / 0.056

FV= $336,091.14

Now, if the deposits are made at the beginning:

FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}

FV= 336,091.14 + [(2,400*1.056^40) - 2,400]

FV= 336,091.14 + 18,821.10

FV= $354,912.24

Difference= 354,912.24 - 336,091.14

Difference= $18,821.1

If the deposits are made at the beginning of the year, the future value will increase by $18,821.1.-