Answer:
The monthly payment is $262.95
Step-by-step explanation:
* Lets explain how to solve the problem
- Omar has decided to purchase an $11,000 car
- He plans on putting 20% down toward the purchase
* Lets find the value of the 20%
∵ The principal value is $11000
∴ the value of the 20% = 20/100 × 11000 = 2200
∴ He will put $2200 down
* Lets find the balance to be paid off on installments
∴ The balance = 11000 - 2200 = 8800
- He financing the rest at 4.8% interest rate for 3 years
* Lets find the rule of the monthly payment
∵
, where
- pmt is the monthly payment
- P = the investment amount
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
∵ P = 8800
∵ r = 4.8/100 = 0.048
∵ n = 12
∵ t = 3
∴ ![pmt=\frac{\frac{0.048}{12}[8800(1+\frac{0.048}{12})^{3(12)}]}{(1+\frac{0.048}{12})^{3(12)}-1}](https://tex.z-dn.net/?f=pmt%3D%5Cfrac%7B%5Cfrac%7B0.048%7D%7B12%7D%5B8800%281%2B%5Cfrac%7B0.048%7D%7B12%7D%29%5E%7B3%2812%29%7D%5D%7D%7B%281%2B%5Cfrac%7B0.048%7D%7B12%7D%29%5E%7B3%2812%29%7D-1%7D)
∴ ![pmt=\frac{0.004[8800(1.004)^{36}]}{(1.004)^{36}-1}=262.95](https://tex.z-dn.net/?f=pmt%3D%5Cfrac%7B0.004%5B8800%281.004%29%5E%7B36%7D%5D%7D%7B%281.004%29%5E%7B36%7D-1%7D%3D262.95)
* The monthly payment is $262.95