mcqs Math Simple Interest Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan. 7984

Question: Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 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) = $6800

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $12240

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $12240 – $6800 = $5440

Thus, Simple Interest = $5440

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5440}/_{6800 × 8}

= ⁵⁴⁴⁰⁰⁰/₅₄₄₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $6800

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $5440 (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 = 8% of Principal

= 8% of $6800

= ⁸/₁₀₀ × 6800

= ^{8 × 6800}/₁₀₀

= ⁵⁴⁴⁰⁰/₁₀₀ = 544

Thus, simple Interest for 1 year = $544

Now,

∵ If the simple Interest is $544, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₄ years

∴ If the simple Interest is $5440, then the time = ¹/₅₄₄ × 5440 years

= ^{1 × 5440}/₅₄₄ years

= ⁵⁴⁴⁰/₅₄₄ = 10 years

Thus, time (T) = 10 years Answer