Question

Investment Analysis

To finance the purchase of a multifamily property 12 years ago, your investment group took a 40-year fixed-rate mortgage (FRM) at an annual interest rate of 3.8%. You are making a payment of $10,000 per month for this mortgage.

A) What is the initial loan amount? (5 points)

B) Suppose this loan is a conventional loan that required an initial 80% LTV. What was the purchase price of the property? (5 points)

C)How much of the next (i.e. t=145) monthly payment will go towards interest and principal? (10 points)

(Please how work and calculations)

Answer 1

A) Initial loan amount

is the PV at the start year of the loan,of the $ 10000 per month payments for a period of 40*12= 480 months at 3.8% p.a. ie. 0.3167%   or 0.003167 p.m

Using the formula, to find PV of loan

PV of mortgage= Pmt.*(1-(1+r)^-480)/r

Filling up the frmula, with the above inputs ,in place,

ie.PV of mortgage=10000*(1-1.003167^-480)/0.003167

2465415.81

B. LTV= 80%

that means,Mortgage amt./Property Value=80%

ie. 2465416/Property value=80%

so, property value or purchase price of property=

2465416/80%=

3081770

C. To answer C. we need to know the remaining loan principal balance, after the (12 yrs,*12 mths.) 144th payment

ie. Remaining Loan balance=FV of the original Principal at end of 144 th pmt.-FV of annuity of the 144 mthly. Pmts.

ie. Rem. Loan bal.= FV of a single sum of $ 2465416 at end of 144 th pmt. -FV of annuity of $10000 at end of 144 the pmt.----------both at 0.3167% p.m.

ie. (2465416*(1.003167)^144)-((10000*(1.003167^144-1)/0.003167)=

2066262.49

Now we can answer

How much of the next (i.e. t=145) monthly payment will go towards interest and principal

ie . Amt. paid towards interest =2066262*0.003167= $ 6543.85

& Amt. paid towards Principal=10000-6543.85= $ 3546.15