Answer to Question #119935 in Financial Math for Piya

Question

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house?
B. Find the value of the monthly payment?
C. Find the loan outstanding after making 20 payments?
D. Find the principal repaid in the 21st payment?

Answer 1

a) value of the mortgage on the house

$value=house value-deposit made$

$value of mortgage=326000-75000$

value of the mortgage is $ 251000

b) value of the monthly payment

$A=\LARGE P {r(1+r)^n \above{2pt} (1+r)^n-1 }$

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$A=\LARGE 251000 {0.0075(1+0.0075)^(360 )\above{2pt} (1+0.0075)^(360)-1 }$

$A=\LARGE 251000 {0.1105 \above{2pt} 14.7306-1 }$

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$A=\LARGE 251000 {0.1105 \above{2pt} 13.7306 }$

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$A= 250000*0.008048$

$A=2020$

value of monthly payment is $ 2020

c) Loan outstanding after 20 payments

20 payments is equal to $ 40400

$Outstanding loan amount= (2020*30*12)-40400$

Outstanding loan amount is $ 686,800

d) Installment repayment amount is $2020

Loan amount owed at 21 months is $ 248054

$principal= monthly installment-(amount owed*rate)$

$principal= 2020-(248054*0.0075)$

$principal= 2020-1860.405$

$principal= 159.595$

Principal amount is equal to $ 159.60