Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9360

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 = $9360 – $6000 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{6000 × 7}

= ³³⁶⁰⁰⁰/₄₂₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3360 (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 = 7% of Principal

= 7% of $6000

= ⁷/₁₀₀ × 6000

= ^{7 × 6000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₂₀ × 3360 years

= ^{1 × 3360}/₄₂₀ years

= ³³⁶⁰/₄₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

(9) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.