mcqs Math Simple Interest James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan. 8018

Question: James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 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) = $4000

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

Amount (A) = $8000

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8000 – $4000 = $4000

Thus, Simple Interest = $4000

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4000}/_{4000 × 10}

= ⁴⁰⁰⁰⁰⁰/₄₀₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $4000

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

Simple Interest = $4000 (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 $4000

= ¹⁰/₁₀₀ × 4000

= ^{10 × 4000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = 400

Thus, simple Interest for 1 year = $400

Now,

∵ If the simple Interest is $400, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₀ years

∴ If the simple Interest is $4000, then the time = ¹/₄₀₀ × 4000 years

= ^{1 × 4000}/₄₀₀ years

= ⁴⁰⁰⁰/₄₀₀ = 10 years

Thus, time (T) = 10 years Answer