Finance Project Spring 2018: Mortgage and Auto Loan Calculations

This finance project involves calculating various aspects of home and auto loans. It begins with determining the financing required for a house after a 20% down payment on a $350,000 property, followed by calculating the Equated Monthly Installment (EMI) for a 30-year loan at 4.25% interest and a 15-year loan at 4% interest. The project also calculates the interest amount on the first payment, the amount owed after 10 years, total payments, and interest payments over the loan term. It further explores the savings achieved by refinancing from a 30-year to a 15-year loan. Additionally, the project covers the financing of an automobile, calculating the amount to be financed after a trade-in, the EMI for a 5-year loan at 3.25% interest, total payments, and the interest payment on the auto loan. The assignment provides a comprehensive overview of loan calculations and financial analysis related to purchasing a home and a vehicle.

EXPLORATION IN MATHEMATICS
STUDENT ID:
[Pick the date]

The link to the property is indicated below.
https://denver.coloradohomefinder.com/homes/7695-Barbara-Ann-Drive/Arvada/CO/
80004/82134926/
Question 1
The asking price for the house is $350,000.
Question 2
Downpayment = (20/100)*350000 = $ 70,000
Hence, financing required to buy the house = 350000 – 70000 = $ 280,000
Question 3
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $280,000, N= 30 years or (30*12 = 360 months), R= 4.25% p.a. or
(4.25/12 = 0.354% per month)
Hence, EMI = 280000*(0.00354)*(1.00354)360/[(1.00354)360-1] = $1,377.43
Question 4
Interest amount on first payment= (0.354/100)*280000 = $ 991.67
Question 5
The amount owed on the house after 10 years would amount to $214,342.2. This has been
obtained by deducting the total principal repayments from the original principal amount of
$280,000.
Question 6
Total payment for the 30 year loan = 1377.43*360 = $495, 875.4

Question 7
Interest payment on the loan = Total payment – Principal amount = 495, 875.4 - 280,000 = $c
Question 8
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $280,000, N= 15 years or (15*12 = 180 months), R= 4% p.a. or (4./12
= 0.333% per month)
Hence, EMI = 280000*(0.00333)*(1.00333)180/[(1.00333)180-1] = $2,071.13
Question 9
Interest amount on first payment= (0.333/100)*280000 = $ 933.33
Question 10
Total payment for the 15 year loan = 2071.13*180 = $372,802.7
Question 11
Interest payment on the loan = Total payment – Principal amount = 372,802.7 - 280,000 =
$92,802.7
Question 12
Money saved by refinancing = Difference in the interest payments = $215,875.4 - $92,802.7
= $123,072.7
The link for the automobile is as follows.
https://www.cargurus.com/Cars/l-Used-BMW-m3#listing=198034044
Question 13

The asking price for the automobile is $30,750.
Question 14
Trade in amount = $6,500
Amount to be financed = 30750 – 6500 = $24,250
Question 15
The formula for EMI (Equal monthly instalment) is indicated below.
EMI = [P x R x (1+R)N]/[(1+R)N-1]
For the given case, P= $24,250, N= 5 years or (5*12 = 60 months), R= 3.25% p.a. or (3.25/12
= 0.271% per month)
Hence, EMI = 24250*(0.00271)*(1.00271)60/[(1.00271)60-1] = $ 438.44
Question 16
Total payment for the 5 year loan = 438.44*60 = $26,306.4
Question 17
Interest payment on the loan = Total payment – Principal amount = 26,306.4 – 24,250 =
$2,056.4