Question

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

A. $35,008.24
B. $92,459.08
C. $105,623.10
D. $88,459.08

Kaitlyn hopes to attend a college where tuition is $24,000 per year. She believes that tuition will increase at 4% for the 3 years until she plans to enter college. Find the quarterly payments needed to accumulate funds to pay the first year’s tuition if funds earn 8% compounded quarterly.
A. $1,597.20
B. $34.05
C. $2,012.87
D. $2,561.30

Answer 1

Results are below.

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