Question

To help you reach a $5,000 goal in five years from now, your father offers to give you $500 now. You plan to get a part-time job and make five additional deposits, one at the end of each year for 5 years. Your first deposit will be made at the end of the first year. If all the money is deposited in a bank that pays 7% interest, how much must your annual deposit be at the end of each year to get $5,000 at the end of 5 years?

Answer 1

Answer:

He needs to deposit each year $747.38

Explanation:

Giving the following information:

To help you reach a $5,000 goal in five years from now, your father offers to give you $500 now. You plan to get a part-time job and make five additional deposits, one at the end of each year for 5 years. Your first deposit will be made at the end of the first year. The money is deposited in a bank that pays 7% interest.

First, we need to calculate the final value of the first $500 that the father gave him:

FV= PV*(1+i)^n

FV= 500*(1.07)^5=

FV= 701.28

Now, we have to calculate the annual deposit required:

Difference= 5,000 - 701.28= 4,298.72

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= (4,298.72*0.07)/[(1.07^5)-1]

A= $747.38