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) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(2) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

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

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(6) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?