suppose that you decide to borrow $16,000 for a new car. you can select one of the following loans, each…

suppose that you decide to borrow $16,000 for a new car. you can select one of the following loans, each requiring regular monthly payments. installment loan a: three - year loan at 6.3% installment loan b: five - year loan at 4.8% use pmt = \\(p\\frac{r/n}{1-(1 + \\frac{r}{n})^{-nt}}\\) to complete parts (a) through (c) below. a. find the monthly payments and the total interest for loan a. the monthly payment for loan a is $ (do not round until the final answer. then round to the nearest cent as needed.)

suppose that you decide to borrow $16,000 for a new car. you can select one of the following loans, each requiring regular monthly payments. installment loan a: three - year loan at 6.3% installment loan b: five - year loan at 4.8% use pmt = \\(p\\frac{r/n}{1-(1 + \\frac{r}{n})^{-nt}}\\) to complete parts (a) through (c) below. a. find the monthly payments and the total interest for loan a. the monthly payment for loan a is $ (do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the values for Loan A

$P = 16000$, $r=0.063$ (annual interest rate), $n = 12$ (month - compounding), $t = 3$ (years)

Step2: Calculate the monthly interest rate

$i=\frac{r}{n}=\frac{0.063}{12}=0.00525$

Step3: Calculate the number of payments

$nt=12\times3 = 36$

Step4: Use the loan - payment formula

$PMT=\frac{P\times i}{1-(1 + i)^{-nt}}=\frac{16000\times0.00525}{1-(1 + 0.00525)^{-36}}$ First, calculate $(1 + 0.00525)^{-36}\approx0.83077$. Then $1-(1 + 0.00525)^{-36}=1 - 0.83077 = 0.16923$. And $16000\times0.00525 = 84$. So $PMT=\frac{84}{0.16923}\approx496.36$

Step5: Calculate the total amount paid

Total amount paid $=PMT\times nt=496.36\times36 = 17868.96$

Step6: Calculate the total interest

Total interest $=17868.96 - 16000=1868.96$

Answer:

The monthly payment for Loan A is $$496.36$ and the total interest for Loan A is $$1868.96$