Question

Auntie Kitty sells her home for $150,000, which is then invested to earn 5 percent annually. If her life expectancy is five years, what is the maximum amount she can annually spend on a nursing home, doctors, and taxes? Use Appendix D to answer the question. Round your answer to the nearest dollar.
The maximum amount that can be annually spend is $ ______

If the return were to double to 10 percent, will the amount she may spend each year more than double? Use Appendix D to answer the question. Round your answer to the nearest dollar.
If the return were to double, the amount that can be annually spent will double, less than double, or more than double, l and will be equal to $ _____

Answer 1

Part A:

PV of Annuity:

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

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

Particulars	Amount
PV Annuity	$      1,50,000.00
Int Rate	5.000%
Periods	5

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 150000 / [ 1 - [(1+0.05)^-240]] /0.05
= $ 150000 / [ 1 - [(1.05)^-240]] /0.05
= $ 150000 / [ 1 - 0.7835 ] /0.05
= $ 150000 / [0.2165 / 0.05 ]
= $ 150000 / 4.3295
= $ 34646.22

Part B:

Particulars	Amount
PV Annuity	$      1,50,000.00
Int Rate	10.000%
Periods	5

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 150000 / [ 1 - [(1+0.1)^-240]] /0.1
= $ 150000 / [ 1 - [(1.1)^-240]] /0.1
= $ 150000 / [ 1 - 0.6209 ] /0.1
= $ 150000 / [0.3791 / 0.1 ]
= $ 150000 / 3.7908
= $ 39569.62

If the Int doubles, Amount that can be spend each year will not be doubled.

ratio = New amount/ Old Amount

=$ 39569.62 / $ 34646.22

= 1.14

Hence Amount is Less than Docuble

Amount that can be specnd is $ 39569.62