Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $6936

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 = $6936 – $5100 = $1836

Thus, Simple Interest = $1836

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 × 1836}/_{5100 × 6}

= ¹⁸³⁶⁰⁰/₃₀₆₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5100

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

Simple Interest = $1836 (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 $5100

= ⁶/₁₀₀ × 5100

= ^{6 × 5100}/₁₀₀

= ³⁰⁶⁰⁰/₁₀₀ = 306

Thus, simple Interest for 1 year = $306

Now,

∵ If the simple Interest is $306, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₆ years

∴ If the simple Interest is $1836, then the time = ¹/₃₀₆ × 1836 years

= ^{1 × 1836}/₃₀₆ years

= ¹⁸³⁶/₃₀₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(3) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.

(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.

(8) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?