1 Attachment(s)

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?

**My Answer:**

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:

Attachment 29628

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

x= $4449.28

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

Code:

`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

******Notice 4048.11 + 401.17 = 4449.28, the amount that you calculated.

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)