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nirvana33 [79]
3 years ago
11

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 scho

ol 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
Business
1 answer:
kari74 [83]3 years ago
5 0

Answer:

Annual deposit= $2,984.69

Explanation:

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

FV= PV*(1+i)^n

FV= 10,000*(1.12^4)

FV= $15,735.19

<u>Now, the annual deposit to cover the difference:</u>

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

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