Question

What is the amount of the payments that Morgan Winslow must make at the end of each of 10 years to accumulate a fund of $93,000 by the end of the 10th year, if the fund earns 10% interest, compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Payment at the end of each year

$

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Part 2

John Hitchcock is 43 years old today and he wishes to accumulate $469,000 by his 67 th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 43 th through his 66 th birthdays. What annual deposit must John make if the fund will earn 10% interest compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Annual deposit

$

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Part 3

Julia Ross has $20,200 to invest today at 12% to pay a debt of $62,738. How many years will it take her to accumulate enough to liquidate the debt? (Round answer to 0 decimal places, e.g. 45.)

What is the amount of the payments that Morgan Winslow must make at the end of each of 10 years to accumulate a fund of $93,000 by the end of the 10th year, if the fund earns 10% interest, compounded annually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Payment at the end of each year

Part 4

Cindy Houston has a $25,900 debt that she wishes to repay 3 years from today; she has $18,435 that she intends to invest for the 3 years. What rate of interest will she need to earn annually in order to accumulate enough to pay the debt? (Round answer to 0 decimal places, e.g. 7%.)

Rate of interest

Answer 1

Part 1:

Accumulated fund at the end of 10 years, F = $93,000

Interest Rate, I = 10%

Let Payment at the end of each year be A

F = A * [FVAF (10%, 9) + 1]

$93,000 = A * [14.93742 + 1]

$93,000 = A * 15.93742

A = $93,000 / 15.93742

A = $5,835

Payment at the end of each year = $5,835

Part 2:

Accumulated amount at the end of 24 years (43 to 67 years), F = $469,000

Interest Rate, I = 10%

Let Payment at the beginning of each year be A

F = A * FVAF (10%, 10)

$469,000 = A * 17.53117

A = $469,000 / 17.53117

A = $26,752

Annual Deposit = $26,752

Part 3:

Investment today, P = $20,200

Interest Rate, I = 12%

Debt, F = $62,738

Let Number of years of investment be n

P (1+I)ⁿ = F

$20,200 (1+0.12)ⁿ = $62,738

(1+0.12)ⁿ = $62738 / $20200

(1+0.12)ⁿ = 3.10584158

FVIF(12%,n) = 3.10584158

n = 10

Number of years required to liquidate the debt = 10 years

Part 4:

Debt, F = $25,900

Number of years to clear debt, n = 3

Investment, P = $18,435

Let interest rate be i

P (1+I)ⁿ = F

$18,435 (1+I)³ = $25,900

(1+I)³ = $25900 / $18435

(1+I)³ = 1.40493626254

1+I = 1.12000232568

I = 0.12000232568 = 12%

Rate of Interest = 12%