Simple Interest
MCQs Math

Question:     Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10608

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10608 – $6800 = $3808

Thus, Simple Interest = $3808

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3808}/_{6800 × 7}

= ³⁸⁰⁸⁰⁰/₄₇₆₀₀

= 8 years (using formula)

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

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6800

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $6800

= ⁷/₁₀₀ × 6800

= ^{7 × 6800}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = 476

Thus, simple Interest for 1 year = $476

Now,

∵ If the simple Interest is $476, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₆ years

∴ If the simple Interest is $3808, then the time = ¹/₄₇₆ × 3808 years

= ^{1 × 3808}/₄₇₆ years

= ³⁸⁰⁸/₄₇₆ = 8 years

Thus, time (T) = 8 years Answer