# CFA 2013 mock morning Q 15

I have been trying hard to figure how do we get the P&I amount given in the solutions using a calculater. I have a BA II plus. I tried entering the values given but I am missing someting. I’d appreciate if someone could help me figure it out.

Thanks.

Its just the payment on an annuity paid monthly.

N= number of months

PV is the current value of the securities

I/Y is the Monthly interest rate so take the WAC and divide it by 12

FV = 0

Compute PMT

I’d post the numbers but I don’t know if CFAI would be ok with that.

This does not get you P&I, it only gets you P. However, the “I” is irrelevant in this question so this method would suffice for the first period. It needs to be done again for the second period by reducing “N” by 1. These two amounts (in addition to the prepayments) are the amounts by which you reduce the principal.

cgottuso8190,

I’m pretty sure that calculation DOES get you the P&I. To get the P, we can multiply (WAC/12) by the Carrying Amount. Then, to get the prepayments for the period, we use this formula: SMM = (Prepayments)/(Carrying Amount - Scheduled Principle Prepayments). In this case, the “Prepayments” is the unkown, so we solve for that. Finally, we add the P amount with the Prepayments and subtract this Total from the current Carrying Value, which get us the next period’s carrying amount.

Hope that makes sense.

This does give you P&I. The PMT solved for gives the amortization payment asssuming no prepayments. You subtract the interest off the P&I PMT calculated to get the scheduled principal payment. The only reason it needs to be done again in the second period is because there was a prepayment which will change the annuity payment.

Sure does, switched FV and PV. Mistakes like this, this late in the game, make me want to put my head through a wall.

I did enter the values as they were given to solve for PMT but I am getting a different answer. I had changed my calculator battery the night before so might just have messed up with the settings.

Thanks for the help guys and all the best for your preperations.

I keep getting the wrong number in the calculator as well. Something like \$480,000 for monthly PMT for . This is something that would normally in my wheel house and find frustrating? I know I must be misisng something simple here…

442, have you solved this problem? I am getting the same thing, calculator malfunction ?!!?

any ideas? I downloaded an app on my phone to confirm that my calculator was working properly…it was

You may be doing the same thing I was at first. I was entering my interest rate as .004 (percentage) rather than .4 (decimal - what the calculator uses. Took me an hour to realize my mistake

Yes that was a mistake I was making…but still not getting the right answer. off by 200k.

N = 243

I/Y = 4.8/12 = .4

PV = -117.54

FV = 0

Cpt PMT = .522 (522 grand) but the solution says the Principal + interest is 757k

I’m so used to calculating interest in decimal format I forgot about the I/Y format in the calculator

this was a tricky q

That is strange, as your inputs should yield the correct answer with the fixed interest rate. I might suggest just resetting your calculator if you have the option? Also, sometimes it just helps to clear the tvm settings a couple times for good measure. Don’t know why but sometimes ill get a strange answer before I have cleared the tvm for a new problem. Sorry I couldn’t be more help, I was sure it was the interest rate that was throwing you off

I’m stuck on this problem and it’s driving me insane… for some reason, I keep getting an answer close to their “A” choice when “B” is the correct answer… I’ll walk through my calculations:

Time 0:

PV = 117.54

N = 243

I = 4.8/12 = 0.4

FV = 0

Compute PMT … it gets -0.75717

Interest = 117.54*0.004 = 0.47016

Prepayment due to SMM = 0.007*117.54 = 0.82278 (they got 0.820771 in the answer key, don’t know why)

Time 1:

PV = 117.54 + 0.47016 - 0.75717 - 0.82278 = 116.43

N =242

I = 0.4

FV = 0

Computer PMT… = -0.75186

Interest = 116.43*0.004 = 0.46572

SMM Prepayment = 0.007*116.43 = 0.81501 (vs. 0.813022 in the answer key)

Month 2 value = 116.43 + 0.46572 - 0.75186 - 0.81501 = 115.329 (answer A, which is incorrect.)

Any ideas what went wrong? my SMM calculations don’t seem to match the answers but I’m not sure why.

Montly prepayment amount = (Beginning outstanding balance - scheduled principal payment) * SMM Scheduled principal payment = Monthly repayment (P+I) - Interest You forgot to deduct scheduled principal payment, rewriting your statement: Prepayment due to SMM = 0.007* (117.54 - 0.287014 ) = 0.820771

By the way, could anyone tell me why the monthly instalment dfifer in month 1 and month 2.

I used to work in mortgage department, for a single loan, you pay a fixed instalment amount per month for the whole loan tenure right?