Answered

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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.)

Sagot :

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:

[tex]PMT=\frac{P_O(\frac{r}{n})}{(1-(1+\frac{r}{n})^{-nt})}[/tex]

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

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

ANSWER:

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

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