Question

Gifford has an annuity that pays $125 at the beginning of each month. If the economy grows at a rate of 3.89% annually, what is the value of the annuity if he received it in a lump sum now rather than over a period of ten years?

Answer 1

I found the future value but an unsure how to calculate the "lump sum now"

Answer 2

For a lump sum,
FV = PV*(1+r)^n
n=number of years,
r=growth rate
So PV from FV
\(PV = \dfrac{FV}{(1+r)^n}\)

Answer 3

Future value is $12,233, correct? @mathmate

Answer 4

$12233 does not sound right.
10 years at 125 per month already gives a capital of
125*10*12=$15000.

Answer 5

What formula do you use? @mg_omg

Answer 6

The problem is a little tricky, because payments are monthly, and interest is annually 3.89%.

Answer 7

@mg_omg are you there?
If you respond, we can do it faster.

Answer 8

I used the future value formula

Answer 9

but i think I got the answer, so nvm

Answer 10

thank you though

Answer 11

which is?

Answer 12

The PV is close to what you got in "Future value is $12,233, correct"

Answer 13

There are two ways to calculate the monthly payment.
1. Put them in a pot, and credit 1500 at the end of a year. Banks used to do this at the time when they didn't use computers. But why would the client pay every month and not get anything out of it till the end of the year? The bank gets to use the money during the year.
So
FV=1500*(1.0389^10-1)/0.0389=17917.56
PV(lump sum)=FV/(1.0389^10)=12233.24, as you had it.

2. Today, banks pay interest on the monthly payments, to the extent of equivalent to 3.89% annually.
The equivalent monthly interest is amortized over 12 months, so
equivalent monthly interest, \(\Large = e^{\frac{log(1.0389)}{12}}-1=0.03185267\), or R=1+0.03185267=1.03185267
This will then be applied over 120 months, i.e.
FV = 125(1.03185267^120/0.03185267)=18234.8182
from which PV=FV/(1.0389^10)=12449.85

You will have to check with your teacher which method of paying interest is expected.