Equivalent Payment Streams
Marvin was supposed to make three payments of $2,500 each — the first one year ago, the second one year from now, and the third three years from now. He missed the first payment and proposes to pay $3,500 today and a second amount in two years. If money can earn 5.5% compounded semiannually, what must the second payment be to make the proposed payments equivalent to the scheduled payments?
I'm trying to solve for x, which is the second payment that is to be made in 2 years from now. I drew a timeline to explain the scenario.
Basically, all the payments in the first stream (Option 1) must be moved to 2 years to make sure they will equal the same amount of money paid in Stream B (option 2)
View the timeline I drew:
Since it is semi-annually, interest is compounded 2x a year. And 5.5%=2.75% per compounding period.
FV1 + FV2 + PV = X + $3500
FV1 = 2500(1.0275)2 = 2639.39
FV2 = 2500(1.0275)6= 2941.92
PV = 2500(1.0275)-2= 2367.97
However, the answer checker says this answer is WRONG. I don't understand why because I followed all the examples in the textbook properly.
Where did I go wrong?? I even used the Financial App on my calculator where you just input the values, and they match my values but answer x is still calculating wrong.
Re: Equivalent Payment Streams
******Notice 4048.11 + 401.17 = 4449.28, the amount that you calculated.
YR PAYMENT INTEREST BALANCE
1 2500.00 .00 2500.00
3 2500.00 286.55 5286.55
5 2500.00 605.95 8392.50
2 3500.00 .00 3500.00
4 4048.11 401.17 7949.28 ******
5 .00 443.22 8392.50
So you did everything ok, except 4048.11 is the required payment, the rest being interest.
One GOOD thing from this: you'll NEVER do this again!!
[2500(1.0275^12 - 1) / (1.0275^4 - 1)] / 1.0275^2 - 3500(1.0275^4) = 4048.107946....
Play with that (Wink)