Question

Problem 6-2 Using the appropriate interest table, provide the solution to each of the following four questions by computing the unknowns. Click here to view factor tables

What is the amount of the payments that John Winslow must make at the end of each of 10 years to accumulate a fund of $95,100 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 $

Steve Hitchcock is 39 years old today and he wishes to accumulate $487,000 by his 64th birthday so he can retire to his summer place on Lake Hopatcong. He wishes to accumulate this amount by making equal deposits on his 39th through his 63th birthdays. What annual deposit must Steve 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 $

Cindy Ross has $19,500 to invest today at 12% to pay a debt of $60,564. How many years will it take her to accumulate enough to liquidate the debt? (Round answer to 0 decimal places, e.g. 45.) years

Amy 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

Based on the information available in the question, we can answer as follows:-

Requirement 1:

Future value = Required payments * FVIFA (10%, 10 years)

$95,100 = x * 15.9374

x = $95,100/15.9374

x = $5,967.096

Required payments = $5,967(Rounded)

Requirement 2:-

Future value = Required payments * FVIF of Annuity Due (10%, 25 years)

$487,000 = x * 108.18182

$487,000/108.18182 = $4,501.68

Required payments = $4,501.68(Rounded)

Requirement 3:-

FVIF = Present value * FVIF(12%, x years)

$60,564/$19,500 = FVIF(12%, x years)

3.1058 = FVIF(12%, x years)

Within the Future value table , under 12% , look out for the year that corresponds to 3.1058

Based on the observation, the years that corresponds is 10 years.

Hence, time taken = 10 years.

Requirement 4:-

FVIF = Present value * FVIF(x%, 3 years)

$25,900 = $18,435 * FVIF(x%, 3 years)

$25,900/18,435 = FVIF(x%, 3 years)

1.4049 = FVIF(x%, 3 years)

Within the Future value table , under 3 years , look out for the year that corresponds to 1.4049

Based on the observation, the rate of interest that corresponds is 12%

Hence, Rate of Interest % = 12%

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