Question

John Madison needs $339,200 in 10 years.
How much must he invest at the end of each year, at 9% interest, to meet his needs? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581
Investment Amount ?
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Steve Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. Steve has recently come into an inheritance of $430,800. He estimates that the boat he wants will cost $312,100 when he retires in 6 years
How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment Amount ?
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John Freeman is investing $9,861 at the end of each year in a fund that earns 6% interest.
In how many years will the fund be at $97,599? (Round answer to 0 decimal places, e.g. 45.)
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John Quincy wants to withdraw $34,700 each year for 7 years from a fund that earns 12% interest.
How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)
First withdrawal immediately
First withdrawal year end
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Answer 1

Solution 1:

Future value of annuity = $339,200

n = 10

interest rate = 9%

Annual deposit = $339,200 / Cumulative FV factor at 9% for 10 periods for ordinary annuity

= $339,200 / 15.19293 = $22,326

Solution 2:

Required Future value = $312,100

Interest rate = 8%

Period = 6 years

Let Required investment = P

now

P * (1+0.08)^6 = $312,100

P = $312,100/1.58687 = $196,676

Solution 3:

Future value = $97,599

Interest rate = 6%

annual deposit = $9,861

Let period = n

Now

$9,861 * Cumulative FV factor for ordinary annuity at 6% for n periods = $97,599

Cumulative FV factor for ordinary annuity at 6% for n periods = 9.89747

On reveiw of FV table, this FV factors lies at n = 8 years

Hence in 8 years value of fund will be $97,599.

solution 4:

Annual withdrawl = $34,700

Period (n) = 7 years

Interest rate = 12%

Investment amount, if first withdrawl at year end = $34,700 * Cumulative PV factor at 12% for 7 periods of ordinary annuity

=$34,700 * 4.56376 = $158,362

Investment amount, if first withdrawl immediately = $34,700 * Cumulative PV factor at 12% for 7 periods of annuity due

=$34,700 * 5.11141 = $177,366