Question

A metallurgist purchases a car for total cost including tax and license of $34,395.66. If the metallurgist obtains a 4-year loan at an annual interest rate of 4.2% compounded monthly, what is the monthly car payment (in dollars)? (Round your answer to the nearest cent. See Example 1 in this section.)

PLEASE HELP IM CONFUSED

Answer 1

The total cost of the car = $34395.66

Interest rate r = 4.2% = 4.2/100 = 0.042

Compounding frequency is monthly so r = 0.042/12 = 0.0035

Now number of years t = 4 years = 12 x 4 = 48 payments

And principal amount P = $34395.66

Now we can use the below formula to find the equal amount

PMT = [ p x r x (1+r)^t ] / [(1+r)^t-1]

PMT = [34395.66 x (0.0035) x (1+(0.0035)⁴⁸ ] / [(1+(0.0035)⁴⁸-1]

PMT = [120.3848 x (1.0035)⁴⁸ ] / [(1.0035)⁴⁸-1]

PMT = [120.3848 x (1.18258) ] / [1.18258-1]

PMT = [142.3646] / [0.18258]

PMT = 779.7381 ~ 779.74

So the monthly payment amount = $779.74