USE DECIMALS The price of a new car is $36,000. Assume that an individual makes
ID: 2646831 • Letter: U
Question
USE DECIMALS The price of a new car is $36,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.) (a) What monthly payment will she be required to make if the car is financed over a period of 48 months? Over a period of 60 months?
(b) What will the interest charges be if she elects the 48-month plan? The 60-month plan?
Explanation / Answer
Answer:
The price of a new car = $36,000
Less; Down payment = 36000*25% = $9000
Hence amount financed (Loan amount PV) = 36000-9000 = $27000
A (1) Calculation of monthly payment using the formula for Present value of annuity:
C = PV / [{1-(1+r) ^-n}/r]
C = monthly payment
PV = Present value = 27000
r= Interest rate =6%/12 = 0.5 % = 0.005
n = time = 48 months
Hence,
C =27000 / [{1-(1+0.005) ^-48}/0.005]
=27000 / (0.2129 / 0.005)
= 27000 /42.58
=$634.10
A (2) Calculation of monthly payment using the formula for Present value of annuity:
C = PV / [{1-(1+r) ^-n}/r]
C = monthly payment
PV = Present value = 27000
r= Interest rate =6%/12 = 0.5 % = 0.005
n = time = 60 months
Hence,
C =27000 / [{1-(1+0.005) ^-60}/0.005]
=27000 / (0.258628 / 0.005)
= 27000 /51.7256
=$521.99
B(1) Calculation of interest charge :
Interest charge = Total amount of monthly installments paid - Present value of loan
= ($634.10 *48 Months ) -$27000
= $3436.80
B(1) Calculation of interest charge :
Interest charge = Total amount of monthly installments paid - Present value of loan
= ($521.99 *60 Months ) -$27000
= $4319.40
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