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What are the answers?

X Gcalculator Google Searc x https://newconnect.mheducation.com/flow/connect.html 6 Saved Help Save & Exit Submit John Rider wants to accumulate $65,000 to be used for his daughter\'s college education. He would like to have the amount available on Decem ber 31, 2023. Assume that the funds will accumulate in a certificate of deposit paying 8% interest compounded annually. Ey ofSi. PV of S1. FVA of S1. PVA of $1. EVAD of $1 and PVAD of S1) (Use appropriate factorís) from the tables provided.) Answer each of the following independent questions. Required 1. If John were to deposit a single amount, how much would he have to invest on December 31, 2018? 2. If John were to make five equal deposits on each December 31, beginning on December 31, 2019, what is the required amount of each deposit? 3. If John were to make five equal deposits on each December 31, beginning on December 31, 2018, what is the required amount of each deposit? (For all requirements, Round your final answers to nearest whole dollar amount.) 1. Amount 2. Annuity amount 3. Annuity amount

Solution

Solution 1:

Required amount after 5 years on December 31, 2023 = $65,000

Interest rate = 8%

Time = 5 years

Amount to be invested today = $65,000 * PV Factor at 8% for 5th period

= $65,000 * 0.680583 = $44,238

Solution 2:

Let required annual deposit starting with December 31, 2019 = a

Now

Future value of ordinary annuity = $65,000

a *Cumulative FV factor at 8% for 5 period = $65,000

a * 5.866601 = $65,000

a = $11,080

Hence required amount of each deposit = $11,080

Solution 3:

Let required annual deposit starting with December 31, 2018 = a

Now

Future value of immediate annuity = $65,000

a *Cumulative FV factor at 8% for 5 period for annuity due = $65,000

a * 6.335929 = $65,000

a = $10,259

Hence required amount of each deposit = $10,259