Question

In: Finance

You would like to retire in 45 years. You expect that you will need $80,000 of...

You would like to retire in 45 years. You expect that you will need $80,000 of today’s purchasing power every year during retirement, with the first withdrawal coming in exactly 45 years. You expect to make 30 annual withdrawals from your retirement account. Annual inflation is expected to be 2%, and you can invest your funds at a 9% nominal interest rate.

(a) What will the nominal value of your first withdrawal be?

(b) How much will you need in your retirement account one year prior to your first withdrawal?

(c) What lump-sum payment would you need to make today in order to endow your retirement?

(d) What constant retirement contribution would you need to make for the next 44 years to obtain your retirement goals?

Expert Solution

(a) inflation is rising every year @2%

so nominal value of first instalment = 80000 x (1.02)⁴⁵ = 80000 x 2.4376 = 195008

(b) amount needed in retirement account one year prior to first withdrawal =

we will use here, present value of growing annuity.

g = inflation rate = 2%, i=rate of interest = 9%

PV = P/( i -g) * (1 - (1+r)ⁿ/(1+g)ⁿ )

PV = [80000 /(0.09-0.02) ] * [ 1 - (1+0.02)³⁰/ (1+0.09)³⁰ ]

PV = 1142857.14 * [ 1 - (1.811/13.268)]

PV= 1142857.14 * 0.8635 = $986864.2 ANSWER (b)

( c) LUMP SUM PAYMENT NEEDED TODAY TO ENDOW RETIREMENT

FV = PV (1+0.09)⁴⁴ /(1+0.02)⁴⁴

$986864.2 = PV (44.349 /2.389)

$986864.2 = PV (18.564)

PV = 53160.10 (ANSWER ( c)

(d) Constant contribution would be required to achieve goal of retirement

FV = P/ (i-g)* [( 1 + r)ⁿ/(1+g)ⁿ - 1]

$986864.2 = P/(0.09-0.02)* [ ( 1 + 0.09)⁴⁴/(1+0.02)⁴⁴ - 1]

$986864.2 = P/ (0.07) * [(44.349/2.389) -1 ]

$986864.2 = P (250.912)

P = $ 3933.1088 ANSWER (d)

GO THROUGH, ANY DOUBTS, FEEL FREE TO ASK

jeff jeffy answered 2 years ago

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