Can you help me?

Question

Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 20 years at the given interest rate, compounded annually.
$6000 at 4%

Thank you.

Answer 1

Hi,
If I understand what you’ve written, you want to make equal yearly payments that amount to $6000 at the end of 20 years. The interest will be 4% compounded yearly.
Then you want to find the amount deposited today that would yield that result 20 years at the same interest and compounding rules.

So, the first part is like an annuity in which you want to find the future value FV. It’s very simple to do this on a TI-83 Plus or TI-84 calculator, but apparently people on this site don’t use those tools. So, here goes:

The formula is: FV = R[1+r/m)^n -1]/(r/m) Where R payment, yearly in this case, n is the number of periods, r is the annual rate, m is the number of compoundings per year.
FV = R[1+r/m)^n -1]/(r/m)
= 6000/20[1+.04/1)^20 -1]/(.04/1) = 8933.42
You can just plug that whole thing into your calculator.

Now, to calculate the equivalent lump sum
P = A/(1+r/m)^n Where P is present value, FV, r and m have the same definitions as above.
P = 8933.42/(1+.04)^20 = 4077.10 rounded off

Hope I interpreted that correctly.
Incidentally, if you have a TI-83 Plus or TI-84 you can find out how to do that on my Website. Go to this URL:
www.anglefire.com/pro/fkizer
click of the TI-83 Plus Financial Guide in the navigation bar, and search for “annuity” for the first one and for “compound interest” on the second one.

FE

Answer 2

6.000(1/1.04+1/1.04^2+ ..+1/1.04^20)=
6,000(1/1.04^21-1/1.04)/(-0.04)= $78405.73
Actual value of the payments