SOLUTION: Antonia receives a $10,000 benefit payment at the end of each year. She can invest these payments in an account yielding 4% interest, compounded annually. Assuming she just receive

Algebra ->  Finance -> SOLUTION: Antonia receives a $10,000 benefit payment at the end of each year. She can invest these payments in an account yielding 4% interest, compounded annually. Assuming she just receive      Log On


   

Question 1151154: Antonia receives a $10,000 benefit payment at the end of each year. She can invest these payments in an account yielding 4% interest, compounded annually. Assuming she just received this year’s payment, what is the present value of her next five payments?
A.
$20,352
B.
$41,253
C.
$44,518
D.
$44,815
Answer by MathLover1(20849) About Me  (Show Source):
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Antonia receives a $10000 benefit payment at the end of each year.
She can invest these payments in an account yielding 4% interest, compounded annually. Assuming she just received this year’s payment, what is the present value of her next five payments?
a $10000 benefit payment
r=4%=0.04 interest
n=5 years


Because the equal payments occur at the end of each year, we know we have an ordinary annuity.
The equation for calculating the present value of an ordinary annuity is:
PVOA+=+FV+%28%281+-+%281+%2F+%281+%2B+r%29%5En%29%29+%2F+r%29
PVOA+=+10000+%28%281+-+%281+%2F+%281+%2B+0.04%29%5E5%29%29+%2F+0.04%29
PVOA+=+10000+%2A4.4518
PVOA+=+44518
This PVOA calculation tells you that receiving $44518 today is equivalent to receiving $10000 at the end of each of the next five years, if the time value of money is 4% per year. If the 4% rate is Antonia's required rate of return, this tells you that Antonia could pay up to $44518 for the five-year annuity.
Answer: C. $44518