mcqs Math Simple Interest William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan. 7997

Question: William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 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) = 9% per annum

Amount (A) = $9500

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9500 – $5000 = $4500

Thus, Simple Interest = $4500

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4500}/_{5000 × 9}

= ⁴⁵⁰⁰⁰⁰/₄₅₀₀₀

= 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) = 9% per annum

Simple Interest = $4500 (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 $5000

= ⁹/₁₀₀ × 5000

= ^{9 × 5000}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₀ years

∴ If the simple Interest is $4500, then the time = ¹/₄₅₀ × 4500 years

= ^{1 × 4500}/₄₅₀ years

= ⁴⁵⁰⁰/₄₅₀ = 10 years

Thus, time (T) = 10 years Answer