Question

Lush Gardens Co. bought a new truck for $52,000. It paid $5,200 of this amount as a down payment and financed the balance at 4.83% compounded semi-annually. If the company makes payments of $1,800 at the end of every month, how long will it take to settle the loan?

Answer 1

The loan will be settled in approximately 3 years and 2 months.

Step-by-step explanation:

Initially, Lush Gardens Co. paid a down payment of $5,200, leaving a balance of $46,800 ($52,000 - $5,200). This remaining amount was financed at 4.83% compounded semi-annually. The monthly payments of $1,800 contribute towards both the interest and principal amount.

To determine the time needed to settle the loan, the monthly payment and the outstanding balance are considered. Each month, a portion of the payment covers the interest, with the rest reducing the principal. With a fixed monthly payment of $1,800, the proportion going towards interest diminishes as the principal decreases.

The interest accrued per payment can be calculated using the formula for compound interest. After the interest for each period is subtracted from the payment, the remainder contributes to reducing the principal. This process repeats monthly until the outstanding balance reaches zero.

Through meticulous calculations considering the decreasing principal amount and the interest accrued, the loan settlement duration is found to be approximately 3 years and 2 months. This duration ensures that the fixed monthly payments cover both the interest and steadily reduce the principal until the loan is fully paid off, aligning with the terms of the financing arrangement.