mcqs Math Simple Interest Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan. 8032

Question: Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10800

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10800 – $5400 = $5400

Thus, Simple Interest = $5400

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5400}/_{5400 × 10}

= ⁵⁴⁰⁰⁰⁰/₅₄₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5400

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5400 (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 = 10% of Principal

= 10% of $5400

= ¹⁰/₁₀₀ × 5400

= ^{10 × 5400}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $5400, then the time = ¹/₅₄₀ × 5400 years

= ^{1 × 5400}/₅₄₀ years

= ⁵⁴⁰⁰/₅₄₀ = 10 years

Thus, time (T) = 10 years Answer