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## 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.

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

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Mathematics
3 months
2021-08-17T01:51:14+00:00
2021-08-17T01:51:14+00:00 1 Answers
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## Answers ( )

Answer:Results are below.

Step-by-step explanation:1.

First, we need to calculate the Future Value:FV= {A*[(1+i)^n-1]}/iA= 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)^NPV= 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)^nFV= 24,000*(1.04^3)

FV= $26,996.74

Now, the quarterly payments:FV= {A*[(1+i)^n-1]}/iA= 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