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 $9000 to clear the loan, then find the time period of the loan. 7718

Question: William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 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) = $5000

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

Amount (A) = $9000

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9000 – $5000 = $4000

Thus, Simple Interest = $4000

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4000}/_{5000 × 10}

= ⁴⁰⁰⁰⁰⁰/₅₀₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5000

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 $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 $4000, then the time = ¹/₅₀₀ × 4000 years

= ^{1 × 4000}/₅₀₀ years

= ⁴⁰⁰⁰/₅₀₀ = 8 years

Thus, time (T) = 8 years Answer