Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $6800

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 = $6800 – $4000 = $2800

Thus, Simple Interest = $2800

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 × 2800}/_{4000 × 10}

= ²⁸⁰⁰⁰⁰/₄₀₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 10% per annum

Simple Interest = $2800 (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 = 10% of Principal

= 10% of $4000

= ¹⁰/₁₀₀ × 4000

= ^{10 × 4000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = 400

Thus, simple Interest for 1 year = $400

Now,

∵ If the simple Interest is $400, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₀ years

∴ If the simple Interest is $2800, then the time = ¹/₄₀₀ × 2800 years

= ^{1 × 2800}/₄₀₀ years

= ²⁸⁰⁰/₄₀₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(4) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(5) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.