mcqs Math Simple Interest John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan. 7898

Question: John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 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) = $4400

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

Amount (A) = $7040

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7040 – $4400 = $2640

Thus, Simple Interest = $2640

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2640}/_{4400 × 6}

= ²⁶⁴⁰⁰⁰/₂₆₄₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $4400

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

Simple Interest = $2640 (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 $4400

= ⁶/₁₀₀ × 4400

= ^{6 × 4400}/₁₀₀

= ²⁶⁴⁰⁰/₁₀₀ = 264

Thus, simple Interest for 1 year = $264

Now,

∵ If the simple Interest is $264, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₆₄ years

∴ If the simple Interest is $2640, then the time = ¹/₂₆₄ × 2640 years

= ^{1 × 2640}/₂₆₄ years

= ²⁶⁴⁰/₂₆₄ = 10 years

Thus, time (T) = 10 years Answer