Question 1168513: Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month for 3 1/2 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step by step to find the selling price of the car.
**1. Understand the Problem**
* Kent sold his car to Carolyn.
* Down payment = $1,000
* Monthly payments = $120.03
* Payment period = 3.5 years
* Interest rate = 12% per year, compounded monthly
**2. Calculate the Number of Payments**
* Number of years = 3.5
* Number of months = 3.5 * 12 = 42 payments
**3. Calculate the Monthly Interest Rate**
* Annual interest rate = 12% = 0.12
* Monthly interest rate (r) = 0.12 / 12 = 0.01
**4. Calculate the Present Value of the Monthly Payments**
We need to find the present value (PV) of the annuity (monthly payments). The formula for the present value of an ordinary annuity is:
PV = PMT * [1 - (1 + r)^-n] / r
Where:
* PV = Present value of the annuity
* PMT = Monthly payment = $120.03
* r = Monthly interest rate = 0.01
* n = Number of payments = 42
PV = 120.03 * [1 - (1 + 0.01)^-42] / 0.01
PV = 120.03 * [1 - (1.01)^-42] / 0.01
PV = 120.03 * [1 - 0.65584] / 0.01
PV = 120.03 * 0.34416 / 0.01
PV = 120.03 * 34.416
PV ≈ 4131.05
**5. Calculate the Selling Price**
The selling price is the sum of the down payment and the present value of the monthly payments.
Selling price = Down payment + PV
Selling price = $1,000 + $4,131.05
Selling price = $5,131.05
**Therefore, the selling price of the car was approximately $5,131.05.**
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month
for 3 1/2 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?
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Calculations in the post by @CPhill are incorrect.
The correct values (the answers) are as follows:
Present value (the loan value) is $4100.
The selling price was $4100 + $1000 = $5100.
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