Monthly loan payments Personal Finance Problem Tim Smith is shopping for a used
ID: 2774884 • Letter: M
Question
Monthly loan payments Personal Finance Problem Tim Smith is shopping for a used car. He has found one priced at $4,000. The salesman has told Tim that if he can come up with a down payment of $1,000, the dealer will finance the balance of the price at an annual rate of 9% over 4 years (48 months). Assuming that Tim accepts the dealer's offer, what will his monthly (end-of-month) payment amount be? Use a financial calculator or spreadsheet to help you figure out what Tim's monthly payment would be if the dealer were willing to finance the balance of the car price at an annual rate of 7%?Explanation / Answer
Cost of Used Car P = $ 4000
Down Payment D = $ 1000
Financed Amount L = $ 4000 - $ 1000 = $ 3000
Annual Rate of Interest = 9%
Monthly Interest rate = 9%/12 = 0.0075
Period = 4 years or 4*12 = 48 months
Monthly instalment A = L * [ (r*(1+r)^n) / ((1+r)^n -1)]
Monthly Instalment A = $ 3000 * [ (0.0075 * (1+0.0075)^48)/(1+0.0075)^48 – 1)]
= $ 3000 * [ (0.0075 * (1.0075)^48)/(1.0075)^48 – 1)]
= $ 3000 * [ (0.0075 * 1.4314053333) / (1.4314053333 – 1)]
= $ 3000 * (0.01073554/0.4314053333)
= $ 3000 * 0.0248850424 = $ 74.6551 or $ 74.66 (rounded off)
Monthly Instalment = $ 74.66
Answer (b)
If the financing is done at an annual rate of 7% per annum or monthly rate of 0.00583333
Monthly Instalment = $ 3000 * [ (0.00583333 * (1.00583333)^48)/(1.00583333)^48 – 1)]
= $ 3000 * [ (0.00583333 * 1.32205367) / (1.32205367-1)]
= $ 3000 * (0.007711975/0.32205367) = $ 3000 * 0.02394624
= $ 71.8387 or $ 71.84 (rounded off)
The result of the same calculated using an online EMI calculator is shown below.
EMI Calculator
Top of Form
Loan amount ($):
Annual interest rate:
%
Loan tenure:
months
Bottom of Form
Equated Monthly Installment Result
$71.84
Loan amount ($):
Annual interest rate:
%
Loan tenure:
months
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