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A widow currently has a $82,000 investment that yields 5 percent annually. Can she withdraw $9,000 for the next fifteen years? Use Appendix D to answer the question. Round your answer to the nearest dollar.
The maximum amount that can be withdrawn is $ so she -Select- (can or cannot) withdraw $9,000 for the next fifteen years.
Would your answer be different if the yield were 8 percent? Use Appendix D to answer the question. Round your answer to the nearest dollar.
If the yield is 8 percent the maximum amount that can be withdrawn is $ so she -Select- (can or cannot) withdraw $9,000 for the next fifteen years.

Respuesta :

If yield is 5% , the maximum amount she can withdraw is $7,900 for next fifteen years.

If yield is 8%, the maximum amount she can withdraw is $9,580 for next fifteen years.

What is the PV factor of an annuity?

Given a specific rate of return, or discount rate, an annuity's present value is the current worth of its expected future payments. The present value of the annuity decreases with increasing discount rates. A succession of future annuities' present values are determined using the annuity's present value interest factor. Its foundation is the time value of money principle, according to which a sum of money acquired today is worth more than the same sum received at a later time.

The PV of final annuity

PV = A[ (1+r)ⁿ - 1/ r(1+r)ⁿ]

PV =  $82,000

r = 5 rpa

r = 15 years

So,  $82,000 = A [tex]\frac{(1+0.05)-1}{0.05(1+0.05)^{15} }}[/tex]

$82,000 = A[tex][\frac{1.07893}{0.10395}][/tex]

$82,000 = A [[tex]\frac{82,000}{10.3793}[/tex]]

A = $ 7900

So she can withdraw $7900 for next 15 years.

If yield is 8%

So,  $82,000 = A [tex]\frac{(1+0.08)^{15}-1}{0.08(1+0.08)^{15} }}[/tex]

$82,000 = A[tex][\frac{2.17217}{0.25377}][/tex]

$82,000 = A [8.5596]

A = [tex]\frac{82000}{85596}[/tex]

= $ 9.580

So she can withdraw $9,580 for next 15 years.

To learn more about present value of annuity , visit:

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