Question

Aaron has an annuity that pays him $9200 at the beginning of each year. Assume the economy will grow at a rate of 3.2% annually. What is the value of the annuity if he received it now instead of over a period of 10 years?

Answer 1

77,682.90?

Answer 2

Can you explain this to me please?

Answer 3

I got 106,444.30

Answer 4

@phi can you help me.

Answer 5

I only know 2 formulas

future value = present value times interest
\[ FV = PV(1+i)^n \]
and
\[ FV= pymt \frac{(1+i)^n -1}{i} \]

we are given the payment= 9200 once per year
n is 10 years
interest rate is 3.2% or 0.032
so we can use the 2nd formula to find FV
and then the first formula to find the present value PV

there are other ways to do this, but this way does work.

Answer 6

When I plugged the numbers into the second formula I got 106444.30 Was that what I was supposed to do?

Answer 7

I think you found the future value. But if he gets paid now, he gets the present value

Answer 8

In other words, 106,444.30 is how much he gets after 10 years.

We can find the present value using the 1st formula.

Answer 9

The options are
$80,168.75
$77,682.00
$106,444.30
$109,850.52

When I plugged the numbers into the first formula I got 126062

Answer 10

I got a different number.
FV=PV(1+i)^n

using FV= 106,444.30, 1+i = 1.032 and n=10
106444.30 = PV * 1.032^10

divide both sides by 1.032^10

Answer 11

Oh I see.. So it would be 77682.9

Answer 12

yes, that is what I got. one of your choices almost matches.

Answer 13

Ok. I am going to open a new question. that is going to be along the same lines. I think I understand but I would like to make sure. Would you be willing to help me?

Answer 14

ok

Answer 15

After some googling I found this site
http://www.bankrate.com/calculators/investing/annuity-calculator.aspx

When I fill in withdrawal amount 9200,
interval Yearly
Leave blank Starting Principal
Set Annual Growth Rate: 3.2
Length in years: 10

It comes up with
Withdrawal Amount: $9200.00 Annual Growth Rate: 3.2%
Interval Between Withdrawals: Yearly Length of Annuity: 10 years
Starting Principal: $80168.75

It found a starting principal of 80168.75, which is the answer.

I then looked at your formulas, and found that if I use

annuity due
PVAD= c((1/i)-(1/(i(1+i)^nt)+c

with c= 9200, i= 0.032, and nt= 9 (NOT 10) I get
9200 * (31.25 - 32.25*0.75325) + 9200
= 80,168.75

I don't know why this works with 9 years rather than 10 years...

Answer 16

I will let my teacher know. She also decided there was a flaw in this question.

Answer 17

She actually thinks there is a flaw in the formula.