Question

Jonathon saves $4,000 at the end of each quarter for 10 years. Assume 12% compounded quarterly and find the present value.

Answer 1

Answer:

Results are below.

Step-by-step explanation:

1. First, we need to calculate the Future Value:

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

A= quarterly deposit

n= 10*4= 40

i= 0.12/4= 0.03

FV= {4,000*[(1.03^40) - 1]} / 0.03

FV= $301,605.04

Now, the present value:

PV= FV/(1+i)^N

PV= 301,605.04/(1.03^40)

PV= $92,459.09

2. First, we need to calculate the value of the first year of college:

FV= PV*(1+i)^n

FV= 24,000*(1.04^3)

FV= $26,996.74

Now, the quarterly payments:

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

A= quarterly deposit

Isolating A:

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

i= 0.08/4= 0.02

n= 3*4= 12

A= (26,996.74*0.02) / [(1.02^12) - 1]

A= $2,012.87