Question

Suppose that you are considering a conventional, fixed-rate 30-year mortgage loan for $100,000. The lender quotes an APR of 7.8%, compounded monthly; mortgage payments would be monthly, beginning one month after the closing on your home purchase. After 15 years of payments, what is the balance outstanding on your loan? Do not round at intermediate steps in your calculation. Round your answer to the nearest penny. Do not type the $ symbol

Answer 1

The formula formula for calculating the monthly EMI on the loan is

EMI= [P x R x (1+R)^N] /  [(1+R)^N-1]

where

P is the Principal Amount

R is the annual rate of interest

N is the number of months

So the values given to us are

P=100000 ; R=7.8% ; N = 15 yr = 180 months

Now putting the values in the formula we get

EMI = [100000*(.078/12)*(1+.078)^180] / [(1+.078/12)^180 - 1 ]

= (100000*.0065*3.2098)/(3.2098-1)

= $ 944.144 This is the monthly EMI of the loan

Now total amount paid in 15 years = 944.14*15*12 = 169945

Loan Amount that has to be paid back in 30 years

We will find this by the formula of compund interest

A = P(1+r/100)^n

Where A is the final amount that has to be repaid

P is the principal amount borrowed = 100000

r is the rate of interest = 7.8% p.a

N is the number of months or years as mentioned = 30 years

A = 100000(1+7.8/(12*100))^360

A = 1030292.45

Hence the amount outstanding or the amount to be paid back will be 1030292.45 - 169945 = 860347.45