What yearly payment will pay off a debt with a 3-year, simple interest term?

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None of these

answer is C.

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Detailed Solution

Concept: Use the idea that the total amount that must be paid over the course of three years to pay off the loan will be the sum of the 1092 principal and the three-year simple interest. If the annual installments are x rupees, then the total for the three years will be 3x rupees. Use

as the direct formula for simple interest as a result. This will assist in finding the solution.
As is common knowledge, simple interest does not accrue interest to the principal over time.
Therefore, the amount (A) that must be paid equals 1092 as the sum of the three-year principal plus simple interest.
Let's say there are X rupees in yearly installments.
Therefore, we were required to pay in three years using three times the regular installments.
As a result,
1092 as the principal + simple interest over the course of three years = 3X……..

.
The current interest rate is 12 percent.
As is common knowledge, the formula for simple interest is

.
where t is the number of years, p is the principal amount, and r is the interest rate.
Therefore, the simple interest for the first year is

.
The premise is still valid in year two: (1092 - X).
Therefore, simple interest for the second year is

The idea still holds true in the third year, or final year: (1092 - 2X)
Therefore, simple interest for the third year is

Using equation

, we now have:

Now, simplifying above equation,

So, this is the yearly payment that must be made in order to pay off the debt of

.
Hence, option 3 is correct.

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