If Sandy Can Afford Car Payments Of 340 P E R M O N T H F O R 4 Y E A R S , W H A T I S T H E P R I C E O F A C A R T H A T S H E C A N A F F O R D N O W ? A S S U M E A N I N T E R E S T R A T E O F 8.7 P E R C E N T . Q U E S T I O N C O N T E N T A R E A B O T T O M P A R T 1 S A N D Y C A N A F F O R D A C A R T H A T C O S T S 340 Per Month For 4 years, What Is The Price Of A Car That She Can Afford Now? Assume An Interest Rate Of 8.7 Percent. Question Content Area Bottom Part 1 Sandy Can Afford A Car That Costs 340 P Er M O N T H F Or 4 Ye A Rs , W Ha T I S T H E P R I Ceo F A C A R T Ha T S H Ec Ana Ff Or D N O W ? A Ss U M E Anin T Eres T R A T Eo F 8.7 P Erce N T . Q U Es T I O N Co N T E N T A Re Ab O Tt O M P A R T 1 S An D Yc Ana Ff Or D A C A R T Ha T Cos T S Enter Your Response
Understanding the Problem
If Sandy can afford car payments of $340 per month for 4 years, we need to calculate the price of a car that she can afford now, assuming an interest rate of 8.7 percent. This problem involves calculating the present value of a future amount, which is a fundamental concept in finance.
Calculating the Total Amount Paid
To calculate the total amount paid, we need to multiply the monthly payment by the number of payments. Since Sandy will be making payments for 4 years, we need to calculate the number of payments first.
- Number of payments = 4 years * 12 months/year = 48 months
- Total amount paid = $340/month * 48 months = $16,320
Calculating the Present Value
The present value of a future amount is the amount that needs to be invested today to receive the future amount, assuming a given interest rate. We can use the formula for present value to calculate the price of the car:
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Present value = $16,320 / (1 + 0.087)^48
- Present value ≈ $10,419.19
Calculating the Price of the Car
The price of the car is equal to the present value, which is approximately $10,419.19. This means that Sandy can afford a car that costs $10,419.19 or less.
Conclusion
In this problem, we calculated the price of a car that Sandy can afford now, assuming an interest rate of 8.7 percent and monthly payments of $340 for 4 years. The present value of the future amount was calculated using the formula for present value, and the price of the car was found to be approximately $10,419.19.
Calculating the Price of a Car with Monthly Payments: Example
Let's consider an example to illustrate the calculation. Suppose Sandy wants to buy a car that costs $15,000. If she can afford monthly payments of $340 for 4 years, we can calculate the interest rate as follows:
- Number of payments = 4 years * 12 months/year = 48 months
- Total amount paid = $340/month * 48 months = $16,320
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Present value = $16,320 / (1 + interest rate)^48
- Interest rate ≈ 0.087 (8.7%)
Calculating the Interest Rate
We can calculate the interest rate using the formula for present value. Rearranging the formula to solve for the interest rate, we get:
- Interest rate = (present value / total amount paid)^(1/number of payments) - 1
- Interest rate ≈ (10,419.19 / 16,320)^(1/48) - 1
- Interest rate ≈ 0.087 (8.7%)
Conclusion
In this example, we calculated the interest rate that Sandy would need to pay to afford a car that costs $15,000, assuming monthly payments of $340 for 4 years. The interest rate was found to be approximately 8.7 percent.
Calculating the Price of a Car with Monthly Payments: Formula
The formula for calculating the price of a car with monthly payments is as follows:
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Price of car = Present value
Conclusion
Q: What is the formula for calculating the price of a car with monthly payments?
A: The formula for calculating the price of a car with monthly payments is as follows:
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Price of car = Present value
Q: How do I calculate the total amount paid?
A: To calculate the total amount paid, you need to multiply the monthly payment by the number of payments. The number of payments is calculated by multiplying the number of years by 12.
- Number of payments = 4 years * 12 months/year = 48 months
- Total amount paid = $340/month * 48 months = $16,320
Q: How do I calculate the interest rate?
A: To calculate the interest rate, you need to rearrange the formula for present value to solve for the interest rate. The formula is as follows:
- Interest rate = (present value / total amount paid)^(1/number of payments) - 1
- Interest rate ≈ (10,419.19 / 16,320)^(1/48) - 1
- Interest rate ≈ 0.087 (8.7%)
Q: What is the present value of a future amount?
A: The present value of a future amount is the amount that needs to be invested today to receive the future amount, assuming a given interest rate.
Q: How do I calculate the present value of a future amount?
A: To calculate the present value of a future amount, you can use the formula for present value, which is as follows:
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Present value = $16,320 / (1 + 0.087)^48
- Present value ≈ $10,419.19
Q: What is the price of a car that Sandy can afford now?
A: The price of a car that Sandy can afford now is approximately $10,419.19, assuming an interest rate of 8.7 percent and monthly payments of $340 for 4 years.
Q: How do I calculate the interest rate that Sandy would need to pay to afford a car that costs $15,000?
A: To calculate the interest rate that Sandy would need to pay to afford a car that costs $15,000, you can use the formula for present value, which is as follows:
- Present value = Total amount paid / (1 + interest rate)^number of payments
- Present value = $15,000 / (1 + interest rate)^48
- Interest rate ≈ 0.087 (8.7%)
Q: What is the total amount paid by Sandy if she can afford monthly payments of $340 for 4 years?
A: The total amount paid by Sandy if she can afford monthly payments of $340 for 4 years is $16,320.
Q: How do I calculate the number of payments?
A: To calculate the number of payments, you need to multiply the number of years by 12.
- Number of payments = 4 years * 12 months/year = 48 months
Q: What is the interest rate that Sandy would need to pay to afford a car that costs $15,000?
A: The interest rate that Sandy would need to pay to afford a car that costs $15,000 is approximately 8.7 percent.