Question

aSuppose you want to buy a new car that costs $32,600. You have no cash-only your old car, which is worth $5000 as a trade-in. The dealer says theinterest rate is 5% add-on for 4 years. Find the monthly paymentThe monthly payment is $(Type an integer or decimal rounded to the nearest cent as needed.)

Answer 1

Given:

Cost of a new car = $32,600

Trade-in old car cost = $5,000

Rate, r = 5% or 0.05

Time, t = 4 years

Asked: Find the monthly payment.

Solution:

`PMT=(P_O((r)/(n)))/((1-(1+(r)/(n))^(-nt)))`

where:

PMT = Loan Payment

Po = Loan Amount

r = Annual Interest Rate

n = Number of Compounds per year

t = Length of the Loan in years

Now that we have the formula, we will substitute the values.

Po = $32,600 - $5,000 = $27,600

r = 5% or 0.05

n = 12 (There are 12 months in 1 year)

t = 4 years

`\begin{gathered} PMT=(P_O((r)/(n)))/((1-(1+(r)/(n))^(-nt))) \\ PMT=(27600((0.05)/(12)))/((1-(1+(0.05)/(12))^(-12\cdot4))) \\ PMT=\frac{115}{(1-0.8190710169^{})} \\ PMT=(115)/(0.1809289831) \\ PMT=635.6085026 \end{gathered}`

ANSWER:

The monthly payment is $636. (Rounded to the nearest cent.)