Question

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

Answer 1

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
 

Answer 2

Alice wants to know how much she'll invest today to receive an annuity of $10,000 for six years if interest is earned at 7% annually.

We will use Annuity Payment formula, which states:

$P=\frac{r (PV)}{1-(1+r)^{-n}}$

where P is the payment,

PV is the present value,

r= rate per period,

n=number of periods.

According to the question,

P = $10,000

r=7%

n=6

We have to find the present value,

Substituting the values in the given formula,

$PV=\frac{P(1-(1+r)^{-n})}{r}$

$PV=\frac{10,000(1-(1.07)^{-6})}{0.07}$

PV= $ 47,665.

So, Alice wants to invest $47,665 today to receive an annuity of $10,000 for six years if interest is earned at 7% annually.