Q:

Alice wants to know how much she'll have to invest today to receive an annuity of $10,000 for six years if interest is earned at 7% annually. She'll make all of her withdrawals at the end of each year. How much should she invest? A. $45,000 B. $47,665 C. $58,333 D. $55,800

Accepted Solution

A:
Annuity formula is given by:
FV=P[(1+r)^n-1]/r
FV=future value
r=rate
n=time
P=principle
Plugging the value from the question we obtain:
FV=10000[(1+0.07)^6-1]/0.07
FV=71,532.91
Thus the current value of the annuity is given by:
A=p(1+r)^n
plugging in the values we obtain and solving for p we get:
71532.91=p(1+0.07)^6
p=71532.91/(1.07)^6
p=$47665.40
Hence the answer:
B] $47665
Β