mcqs Math Simple Interest Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan. 7922

Question: Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 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) = 6% per annum

Amount (A) = $10880

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10880 – $6800 = $4080

Thus, Simple Interest = $4080

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4080}/_{6800 × 6}

= ⁴⁰⁸⁰⁰⁰/₄₀₈₀₀

= 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) = 6% per annum

Simple Interest = $4080 (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 $6800

= ⁶/₁₀₀ × 6800

= ^{6 × 6800}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $4080, then the time = ¹/₄₀₈ × 4080 years

= ^{1 × 4080}/₄₀₈ years

= ⁴⁰⁸⁰/₄₀₈ = 10 years

Thus, time (T) = 10 years Answer