2. The 2018 Toyota Yaris is a popular compact car for young adults. Dealer\"A\"
ID: 2808232 • Letter: 2
Question
2. The 2018 Toyota Yaris is a popular compact car for young adults. Dealer"A" is offering the Toyota Yaris with a $0 down payment and monthly payments of $380 for a 5 year loan at 4.25% APR (interest). Dealer "B" is offering the Toyota Yaris with a $2,000 down payment and monthly payments of $330 for a 5 year loan at 2% APR (interest). a) What is the equivalent cash value of the Toyota Yaris today? Dealer "A" Dealer "B" b) What will be the total amount paid on the loan if the consumerfinances the car? Dealer "A" Dealer "B" How much interest would a consumer pay if s/he finances the car? Dealer "B" c) Dealer AExplanation / Answer
a) Calculation of equivalent cash value
We have
equivalent cash value = Down payment + PV of loan
Present value of Annuity = A*[(1-(1+r)-n)/r]
Where
A - Annuity payment
r - rate per period
n - no. of periods
Equivalent cash value for dealer A = 0 + 380*[(1-(1.0035)-60)/.0035]
= 380*54.0339
= 20,532.88
Equivalent cash value for dealer A = 2,000 + 330*[(1-(1.0017)-60)/.0017]
= 2000+330*56.9954
= 2000+18808.482
= 20,808.48
b) Calculation of total amount paid on loan
Total amount paid on loan = EMI*no. of installments
Total amount paid on loan from dealer A = 380*5*12
= 22,800
Total amount paid on loan from dealer B = 330*5*12
= 19,800
c) Calculation of interest paid on loan
Interest on mortgage = (EMI*no. of installments) - loan amount
Interest on mortgage from dealer A = 22,800 - 20,532.88
= 2,267.12
Interest on mortgage from dealer B = 19,800 - 18,808.48
= 991.52
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