Answer:
A ) Hence The interest for the car loan is $ 4,310
B ) Hence The interest for the car loan is $ 3,152
Step-by-step explanation:
Given as :
The loan for the car = $ 20,000
The rate of interest of car loan = 5 % compounded annually
A ) The period of loan = 48 months = 4 years
Let the interest of the loan = CI
<u>From compounded method</u>
Amount = Principal × ![(1 + \frac{\textrm Rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%20%2B%20%5Cfrac%7B%5Ctextrm%20Rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
Or, Amount = $ 20,000 × ![(1 + \frac{\textrm 5}{100})^{\textrm 4}](https://tex.z-dn.net/?f=%281%20%2B%20%5Cfrac%7B%5Ctextrm%205%7D%7B100%7D%29%5E%7B%5Ctextrm%204%7D)
Or, Amount = $ 20,000 × ![(1.05)^{4}](https://tex.z-dn.net/?f=%281.05%29%5E%7B4%7D)
Or, Amount = $ 20,000 × 1.2155
∴ Amount = $ 24310
So, Interest = Amount - Principal
Or, CI = $ 24,310 - $ 20,000
∴ CI = $ 4,310
Hence The interest for the car loan is $ 4,310
B ) The loan for the car = $ 20,000
The rate of interest of car loan = 5 % compounded annually
The period of loan = 3 years
Let the interest of the loan = CI
So,
<u>From compounded method</u>
Amount = Principal × ![(1 + \frac{\textrm Rate}{100})^{\textrm time}](https://tex.z-dn.net/?f=%281%20%2B%20%5Cfrac%7B%5Ctextrm%20Rate%7D%7B100%7D%29%5E%7B%5Ctextrm%20time%7D)
Or, Amount = $ 20,000 × ![(1 + \frac{\textrm 5}{100})^{\textrm 3}](https://tex.z-dn.net/?f=%281%20%2B%20%5Cfrac%7B%5Ctextrm%205%7D%7B100%7D%29%5E%7B%5Ctextrm%203%7D)
Or, Amount = $ 20,000 × ![(1.05)^{3}](https://tex.z-dn.net/?f=%281.05%29%5E%7B3%7D)
Or, Amount = $ 20,000 × 1.1576
∴ Amount = $ 23,152
So, Interest = Amount - Principal
Or, CI = $ 23,152 - $ 20,000
∴ CI = $ 3,152
Hence The interest for the car loan is $ 3,152