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 $10608 to clear the loan, then find the time period of the loan. 7519

Question: Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(A)  5.25
(B)  8.75
(C)  7
(D)  10.5

Correct Answer 7

Solution And Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10608

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10608 – $6800 = $3808

Thus, Simple Interest = $3808

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3808}/_{6800 × 8}

= ³⁸⁰⁸⁰⁰/₅₄₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6800

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

Simple Interest = $3808 (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 $3808, then the time = ¹/₅₄₄ × 3808 years

= ^{1 × 3808}/₅₄₄ years

= ³⁸⁰⁸/₅₄₄ = 7 years

Thus, time (T) = 7 years Answer