Question

You can afford a $450 per month car payment. You've found a 4

year loan at 6% annual interest rate, compounded monthly. How big
of a loan amount can you afford? (Enter numeric answers to 2
decimal pla

Answer 1

With a $450 per month payment, over 4 years at 6% interest compounded monthly, you can afford a loan amount of $19,644.93.

Step-by-step explanation:

Calculation of Loan Amount Based on Monthly Payment

To calculate the loan amount you can afford with a $450 per month car payment, a 4-year loan duration, and a 6% annual interest rate compounded monthly, we need to use the present value formula for an annuity. This formula is given as:

PV = Pmt[1 - (1 + i)⁻ⁿ]/i

Where:

PV = Present Value (the loan amount)

Pmt = Monthly payment ($450)

i = Monthly interest rate (0.06/12 = 0.005)

n = Total number of payments (4 years * 12 months/year = 48 payments)

Plugging the numbers into the formula, we get:

PV = 450[1 - (1 + 0.005)⁻⁴⁸]/0.005

Calculating the above expression:

PV = $19,644.93

Therefore, you can afford a loan amount of $19,644.93.