Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $12200

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 = $12200 – $6100 = $6100

Thus, Simple Interest = $6100

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 × 6100}/_{6100 × 10}

= ⁶¹⁰⁰⁰⁰/₆₁₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $6100

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

Simple Interest = $6100 (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 $6100

= ¹⁰/₁₀₀ × 6100

= ^{10 × 6100}/₁₀₀

= ⁶¹⁰⁰⁰/₁₀₀ = 610

Thus, simple Interest for 1 year = $610

Now,

∵ If the simple Interest is $610, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₀ years

∴ If the simple Interest is $6100, then the time = ¹/₆₁₀ × 6100 years

= ^{1 × 6100}/₆₁₀ years

= ⁶¹⁰⁰/₆₁₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.

(4) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.

(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.