mcqs Math Simple Interest Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan. 7659

Question: Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(A)  6
(B)  10
(C)  8
(D)  12

Correct Answer 8

Solution And Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8692

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8692 – $5300 = $3392

Thus, Simple Interest = $3392

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3392}/_{5300 × 8}

= ³³⁹²⁰⁰/₄₂₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3392 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 8% of Principal

= 8% of $5300

= ⁸/₁₀₀ × 5300

= ^{8 × 5300}/₁₀₀

= ⁴²⁴⁰⁰/₁₀₀ = 424

Thus, simple Interest for 1 year = $424

Now,

∵ If the simple Interest is $424, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₄ years

∴ If the simple Interest is $3392, then the time = ¹/₄₂₄ × 3392 years

= ^{1 × 3392}/₄₂₄ years

= ³³⁹²/₄₂₄ = 8 years

Thus, time (T) = 8 years Answer