Question

A student wants to have $30,000 at graduation 4 years from now to buy a new car. His grandfather gave him $10,000 as a high school graduation present. How much must the student save each year if he deposits the $10,000 today and can earn 12% on both the $10,000 and his earnings in a mutual fund his grandfather recommends

Answer 1

Annual deposit= $2,984.69

Step-by-step explanation:

First, we need to calculate the Future Value of the lumpsum investment using the following formula:

FV= PV*(1+i)^n

FV= 10,000*(1.12^4)

FV= $15,735.19

Now, the annual deposit to cover the difference:

Difference= 30,000 - 15,735.19= 14,264.81

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

A= annual deposit

Isolating A:

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

A= (14,264.81*0.12) / [(1.12^4) - 1]

A= $2,984.69