Question

Mr. Nelson bought a car for $20,000 with a 5% interest rate.

a.) Mr. Nelson gets a loan to pay the car off in 48 months. How much interest would he have to pay? Show your work. (2 points)

b.) Suppose Mr. Nelson paid the loan off in 3 years. How much interest would he save paying the car off early (3 years instead of 48 months)? Show your work. (2 points)

Answer 1

A ) Hence The interest for the car loan is $ 4,310

B ) Hence The interest for the car loan is $ 3,152

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

From compounded method

Amount = Principal ×
`(1 + (\textrm Rate)/(100))^(\textrm time)`

Or, Amount = $ 20,000 ×
`(1 + (\textrm 5)/(100))^(\textrm 4)`

Or, Amount = $ 20,000 ×
`(1.05)^(4)`

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,

From compounded method

Amount = Principal ×
`(1 + (\textrm Rate)/(100))^(\textrm time)`

Or, Amount = $ 20,000 ×
`(1 + (\textrm 5)/(100))^(\textrm 3)`

Or, Amount = $ 20,000 ×
`(1.05)^(3)`

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