Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 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) = 7% per annum

Amount (A) = $6240

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 = $6240 – $4000 = $2240

Thus, Simple Interest = $2240

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 × 2240}/_{4000 × 7}

= ²²⁴⁰⁰⁰/₂₈₀₀₀

= 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) = 7% per annum

Simple Interest = $2240 (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 $4000

= ⁷/₁₀₀ × 4000

= ^{7 × 4000}/₁₀₀

= ²⁸⁰⁰⁰/₁₀₀ = 280

Thus, simple Interest for 1 year = $280

Now,

∵ If the simple Interest is $280, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₀ years

∴ If the simple Interest is $2240, then the time = ¹/₂₈₀ × 2240 years

= ^{1 × 2240}/₂₈₀ years

= ²²⁴⁰/₂₈₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(2) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?