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 $6512 to clear the loan, then find the time period of the loan. 7588

Question: John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 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) = $4400

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

Amount (A) = $6512

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $6512 – $4400 = $2112

Thus, Simple Interest = $2112

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2112}/_{4400 × 6}

= ²¹¹²⁰⁰/₂₆₄₀₀

= 8 years (using formula)

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

Here, we have

Principal (P) = $4400

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

Simple Interest = $2112 (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 $2112, then the time = ¹/₂₆₄ × 2112 years

= ^{1 × 2112}/₂₆₄ years

= ²¹¹²/₂₆₄ = 8 years

Thus, time (T) = 8 years Answer