Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $8740

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 = $8740 – $4600 = $4140

Thus, Simple Interest = $4140

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 × 4140}/_{4600 × 10}

= ⁴¹⁴⁰⁰⁰/₄₆₀₀₀

= 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) = $4600

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

Simple Interest = $4140 (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 $4600

= ¹⁰/₁₀₀ × 4600

= ^{10 × 4600}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = 460

Thus, simple Interest for 1 year = $460

Now,

∵ If the simple Interest is $460, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₀ years

∴ If the simple Interest is $4140, then the time = ¹/₄₆₀ × 4140 years

= ^{1 × 4140}/₄₆₀ years

= ⁴¹⁴⁰/₄₆₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.