Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $6880

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 = $6880 – $4000 = $2880

Thus, Simple Interest = $2880

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 × 2880}/_{4000 × 9}

= ²⁸⁸⁰⁰⁰/₃₆₀₀₀

= 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) = $4000

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2880 (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 = 9% of Principal

= 9% of $4000

= ⁹/₁₀₀ × 4000

= ^{9 × 4000}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $2880, then the time = ¹/₃₆₀ × 2880 years

= ^{1 × 2880}/₃₆₀ years

= ²⁸⁸⁰/₃₆₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?

(4) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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

(6) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.

(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.