Question

it is very important that you show your work from the calculations (right down what you used as PV, i FV, n, cash flows,.....etc. in your calculation)

Suppose you make $65,000/year. You want to purchase a $300,000 house with a 90% LTV loan. The current 30-year FRM interest rate is at 6.5%. Your monthly insurance and property tax payment add up to $250. The lender allows a maximum Total Housing Expense to Income rate of 35%. Will you qualify for this loan?

Answer 1

Answer:

Given, cost of the house is $300,000 and LTV is 90%. Hence loan intended is $300,000*90% = $270,000

Term of the loan is 30 years and interest rate is 6.5% (fixed)

(a) Monthly repayment of the loan will be $1,706.58 as shown in the screen shot below:

A B C D E 1 Constant Payment Mortgage or Equated Monthly Installments (EMI) 2 3 EMI is calculated using the formula EMI=[P*r*(1+r)^n]/[(1+r)^n)-1 4 Where P= Principal (loan amount), 5 n= Number of installments. ie if N= number of years, n=N*12 6 r= Rate of interest per month in decimals ie. If R= Yearly rate, r=R/(100*12) 7 All amounts in $ 8 Given that 9 Principal (loan amount) (P)= 270000 No. of years (N)= 10 Rate of interest (% p.a)=R= 6.5 No. of months (n)= 360 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per month in decimals (r)= R/(100*12) D10/(100*12) 0.005416667 15 No. of months (n)= N*12 G9*12 360 16 (1+r)= 1+G14 1.005416667 17 (1+r)^n= G16^G10 6.991797974 [(1+r)^n)-1= G17-1 5.991797974 19 P*r*(1+r)^n= D9*G14*G17 10225.50454 20 Equated Monthly Insallments (EMI)= [P*r*(1+r)^n]/[(1+r)^n)-1 G19/618 1706.583663 Rounded to $1,706.58 22 21

(b) Given that yearly income = $65,000. Hence monthly income= $65,000/12= $5416.67

(c) Given, monthly insurance and property tax expenses= $250

(d) Total Housing expenses= a + c = $1,706.58 + $250 = $1,956.58

Rate of Total Housing Expenses to income= (d/b)*100 = ($1906.58 / $5416.67)*100 = 36.12%

Since this rate (36.12%) is higher than the maximum of 35% stipulated by the lender, not eligible for the loan.