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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Euphemia 3 months 2021-08-17T01:51:14+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-17T01:52:22+00:00

    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

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