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 $12240 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $12240

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 = $12240 – $6800 = $5440

Thus, Simple Interest = $5440

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 × 5440}/_{6800 × 10}

= ⁵⁴⁴⁰⁰⁰/₆₈₀₀₀

= 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) = 10% per annum

Simple Interest = $5440 (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 $5440, then the time = ¹/₆₈₀ × 5440 years

= ^{1 × 5440}/₆₈₀ years

= ⁵⁴⁴⁰/₆₈₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.

(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(4) 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.

(5) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(8) 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.

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.