mcqs Math Simple Interest Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan. 8001

Question: Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 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) = 9% per annum

Amount (A) = $10260

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10260 – $5400 = $4860

Thus, Simple Interest = $4860

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4860}/_{5400 × 9}

= ⁴⁸⁶⁰⁰⁰/₄₈₆₀₀

= 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) = 9% per annum

Simple Interest = $4860 (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 = 9% of Principal

= 9% of $5400

= ⁹/₁₀₀ × 5400

= ^{9 × 5400}/₁₀₀

= ⁴⁸⁶⁰⁰/₁₀₀ = 486

Thus, simple Interest for 1 year = $486

Now,

∵ If the simple Interest is $486, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₆ years

∴ If the simple Interest is $4860, then the time = ¹/₄₈₆ × 4860 years

= ^{1 × 4860}/₄₈₆ years

= ⁴⁸⁶⁰/₄₈₆ = 10 years

Thus, time (T) = 10 years Answer