Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $6776

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 = $6776 – $4400 = $2376

Thus, Simple Interest = $2376

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 × 2376}/_{4400 × 6}

= ²³⁷⁶⁰⁰/₂₆₄₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4400

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

Simple Interest = $2376 (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 $2376, then the time = ¹/₂₆₄ × 2376 years

= ^{1 × 2376}/₂₆₄ years

= ²³⁷⁶/₂₆₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?