Austin Miller wishes to have $200,000 in a retirement fund 25 years from now. He can...

Austin Miller wishes to have $200,000 in a retirement fund 25 years from now. He can create the retirement fund by making a single lump-sum deposit today. Use next table to solve the following problems.

If upon retirement in 25 years, Austin plans to invest $200,000 in a fund that earns 10%, what is the maximum annual withdrawal he can make over the following 15 years? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
Calculate your answer based on the PVA-factor.
$

Calculate your answer based on the financial calculator.
$
How much would Austin need to have on deposit at retirement in order to withdraw $55,000 annually over the 15 years if the retirement fund earns 10%? Round the answer to the nearest cent. Round PVA-factor to three decimal places.
Calculate your answer based on the PVA-factor.
$

Calculate your answer based on the financial calculator.
$
To achieve his annual withdrawal goal of $55,000 calculated in part b, how much more than the amount calculated in part a must Austin deposit today in an investment earning 10% annual interest? Round PVA-factor to three decimal places. Round your answer to the nearest cent. If an amount is zero, enter "0".
$

Solutions

Expert Solution

PVA Factor method

a	PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate
	PVA factor= (1-1/(1+rate)^number of terms)/rate
	PVA Factor	7.606079506
	Maximum withdrawal	26294.76

b	PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate
	PVA factor= (1-1/(1+rate)^number of terms)/rate
	PVA Factor	7.606079506
	Amount of deposit required	418334.37

c	Difference in final amount	218334.37

	Future Value of annuity = A* ((1+rate)^n-1)/rate
	FVA factor	98.34705943
	Amount of deposits required	2220.039665

WORKINGS

Financial calculator method

1: Using financial calculator

Input: PV = 200000, N = 15, I/Y = 10. Solve for PMT as 26294.76

2: Using financial calculator

Input: PMt = 55000, N = 15, I/Y = 10. Solve for PV as 418334.37

Difference in final amount

218334.37

Using financial calculator

Input FV = 218334.37, N= 25, I/Y = 10 Solve for PMT = 2,220.04

jeff jeffy answered 1 month ago

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