Tom wants to buy a car. He figures he has $200.00 a month to spend on loan payments. The bank's current new car loans are 5.2% for 5 years. Find the amount he can afford to borrow.
To find the amount Tom can afford to borrow, we need to calculate the maximum loan payment he can make each month.
Step 1: Convert the interest rate from a percentage to a decimal.
The interest rate is given as 5.2%. To convert it to a decimal, divide it by 100:
5.2% / 100 = 0.052 (decimal)
Step 2: Determine the number of months in the loan term.
The loan term is given as 5 years. Since there are 12 months in a year, multiply 5 by 12:
5 years * 12 months/year = 60 months
Step 3: Use the loan payment formula to calculate the maximum loan payment.
The formula for calculating the monthly loan payment is:
Loan Payment = Loan Amount x (interest rate / (1 - (1 + interest rate)^(-number of months)))
In this case, the loan payment is $200.00, the interest rate is 0.052, and the number of months is 60. We want to solve for the loan amount.
200 = Loan Amount x (0.052 / (1 - (1 + 0.052)^(-60)))
Step 4: Rearrange the formula to solve for Loan Amount.
Multiply both sides of the equation by (1 - (1 + 0.052)^(-60)) and divide by 0.052:
Loan Amount = 200 / ((0.052 / (1 - (1 + 0.052)^(-60))))
Step 5: Calculate the Loan Amount.
Using a calculator, evaluate the expression:
Loan Amount ≈ 200 / 0.00748
Loan Amount ≈ 26,738.92
Therefore, Tom can afford to borrow approximately $26,738.92 for a new car loan.
To find the amount Tom can afford to borrow, we need to calculate the maximum monthly payment he can make based on his budget and the loan term. Then, we can use this monthly payment to determine the loan amount he can afford.
Step 1: Calculate the maximum monthly payment:
Tom has $200.00 per month to spend on loan payments.
Step 2: Determine the loan term:
The loan term is given as 5 years.
Step 3: Convert the loan term to months:
Since there are 12 months in a year, the loan term of 5 years is equal to 5 * 12 = 60 months.
Step 4: Use the maximum monthly payment to calculate the loan amount:
To calculate the loan amount using the monthly payment, we need to use the formula for the present value of an ordinary annuity.
The formula for the present value of an ordinary annuity is:
PV = PMT * ((1 - (1 + r)^(-n)) / r),
where PV is the present value or loan amount, PMT is the monthly payment, r is the interest rate per month (annual interest rate divided by 12), and n is the number of monthly payments.
Substituting the values we have:
PMT = $200.00
r = 5.2% = 0.052 (converted to decimal)
n = 60
PV = $200.00 * ((1 - (1 + 0.052)^(-60)) / 0.052)
By calculating this expression, we can find the amount Tom can afford to borrow.
Assuming the normally for monthly payments the interest would be compounded monthly
i = .052/12 = .0043333...
n = 5*12 = 60
200( 1 - 1.0043333...^-60)/.0043333.. = PV
PV = $10,546.85