Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11560

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 = $11560 – $6800 = $4760

Thus, Simple Interest = $4760

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 × 4760}/_{6800 × 10}

= ⁴⁷⁶⁰⁰⁰/₆₈₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 10% per annum

Simple Interest = $4760 (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 = 10% of Principal

= 10% of $6800

= ¹⁰/₁₀₀ × 6800

= ^{10 × 6800}/₁₀₀

= ⁶⁸⁰⁰⁰/₁₀₀ = 680

Thus, simple Interest for 1 year = $680

Now,

∵ If the simple Interest is $680, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₈₀ years

∴ If the simple Interest is $4760, then the time = ¹/₆₈₀ × 4760 years

= ^{1 × 4760}/₆₈₀ years

= ⁴⁷⁶⁰/₆₈₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(5) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(10) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.