mcqs Math Simple Interest William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan. 8028

Question: William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 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) = $5000

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

Amount (A) = $10000

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10000 – $5000 = $5000

Thus, Simple Interest = $5000

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5000}/_{5000 × 10}

= ⁵⁰⁰⁰⁰⁰/₅₀₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5000

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

Simple Interest = $5000 (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 $5000

= ¹⁰/₁₀₀ × 5000

= ^{10 × 5000}/₁₀₀

= ⁵⁰⁰⁰⁰/₁₀₀ = 500

Thus, simple Interest for 1 year = $500

Now,

∵ If the simple Interest is $500, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₀ years

∴ If the simple Interest is $5000, then the time = ¹/₅₀₀ × 5000 years

= ^{1 × 5000}/₅₀₀ years

= ⁵⁰⁰⁰/₅₀₀ = 10 years

Thus, time (T) = 10 years Answer