Question

Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of savings, which is invested to earn a guaranteed 5% rate of return. Ignoring the effects of inflation, CONSTRUCT the amortization table for the 15 years, if she withdraws at the beginning of each year and keep the withdrawals constant in nominal terms, until the balance reaches a balance zero at the end of the 15th year. LABEL properly.

Answer 1

Current savings = $ 1000000

first withdrawl at the begining of the year

total payments = 15

PV of Annuity Due:
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period = 5 % or 0.05
n - No. of periods = 15

Particulars	Amount
PV of Annuity Due	$      1,000,000.00
Int Rate	5.000%
Periods	15
PVAF(r%, n-1)	9.8986
[ [ PVAF(r%, n-1) ] + 1 ]	10.8986

Cash Flow = PV of Annuity Due / [ 1 + PVAF (r%, n - 1 ) ]
= $ 1000000 / [ 1 + PVAF ( 5%, 15 - 1 ) ]
= $ 1000000 / [ 1 + 9.8986 ]
= $ 1000000 / [ 10.8986 ]
= $ 91754.56

PVAF (r% , n-1) = 9.8986

r = 5 % or 0.05

n-1 = 15 - 1 = 14

PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.05)^-14]] /0.05
= [ 1 - [(1.05)^-14]] /0.05
= [ 1 - [0.50507]] /0.05
= [0.49493]] /0.05
= 9.8986

if she had $ 1000000 in account she withdraws at the beginning of each year to until the balance reaches a balance zero at the end of the 15th year is $91754.56

Please comment if any further assistance is required.