Simple Interest
Math MCQs

Question :  ( 1 of 10 )  James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6400

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 = $6400 – $4000 = $2400

Thus, Simple Interest = $2400

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 × 2400}/_{4000 × 6}

= ²⁴⁰⁰⁰⁰/₂₄₀₀₀

= 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) = $4000

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

Simple Interest = $2400 (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 $4000

= ⁶/₁₀₀ × 4000

= ^{6 × 4000}/₁₀₀

= ²⁴⁰⁰⁰/₁₀₀ = 240

Thus, simple Interest for 1 year = $240

Now,

∵ If the simple Interest is $240, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₀ years

∴ If the simple Interest is $2400, then the time = ¹/₂₄₀ × 2400 years

= ^{1 × 2400}/₂₄₀ years

= ²⁴⁰⁰/₂₄₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.

(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(10) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.