mcqs Math Simple Interest William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan. 7749

Question: William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(A)  6.75
(B)  11.25
(C)  9
(D)  13.5

Correct Answer 9

Solution And Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7700

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7700 – $5000 = $2700

Thus, Simple Interest = $2700

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2700}/_{5000 × 6}

= ²⁷⁰⁰⁰⁰/₃₀₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2700 (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 = 6% of Principal

= 6% of $5000

= ⁶/₁₀₀ × 5000

= ^{6 × 5000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = 300

Thus, simple Interest for 1 year = $300

Now,

∵ If the simple Interest is $300, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₀ years

∴ If the simple Interest is $2700, then the time = ¹/₃₀₀ × 2700 years

= ^{1 × 2700}/₃₀₀ years

= ²⁷⁰⁰/₃₀₀ = 9 years

Thus, time (T) = 9 years Answer