mcqs Math Simple Interest Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan. 7597

Question: Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 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) = 6% per annum

Amount (A) = $7844

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7844 – $5300 = $2544

Thus, Simple Interest = $2544

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2544}/_{5300 × 6}

= ²⁵⁴⁴⁰⁰/₃₁₈₀₀

= 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) = 6% per annum

Simple Interest = $2544 (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 = 6% of Principal

= 6% of $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $2544, then the time = ¹/₃₁₈ × 2544 years

= ^{1 × 2544}/₃₁₈ years

= ²⁵⁴⁴/₃₁₈ = 8 years

Thus, time (T) = 8 years Answer