Your goal is to have $15,000 in your bank account by the end of four years. If the interest rate remains constant at 4% and you want to make annual identical deposits. If your deposits were made at the beginning of each year rather than an at the end, by how much would the amount of your deposit change if you still wanted to reach your goal by the end of six years?

Your goal is to have $15,000 in your bank account by the end of four years. The interest rate remains constant at 4% and you want to make annual identical deposits.

End of the year:

To calculate the annual deposit, we need to use the following formula:

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

A= annual deposit

Isolating A:

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

A= (15,000*0.04) / [(1.04^4) - 1]= $3,532.35

Beginning of the year:

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

A= 3,532.35/ 1.04= $3,396.49

The difference resides in the interest compounded. At the beginning of the year the interest compound for one more period.