Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $8800

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 = $8800 – $4400 = $4400

Thus, Simple Interest = $4400

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 × 4400}/_{4400 × 10}

= ⁴⁴⁰⁰⁰⁰/₄₄₀₀₀

= 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) = $4400

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

Simple Interest = $4400 (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 $4400

= ¹⁰/₁₀₀ × 4400

= ^{10 × 4400}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $4400, then the time = ¹/₄₄₀ × 4400 years

= ^{1 × 4400}/₄₄₀ years

= ⁴⁴⁰⁰/₄₄₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 8% simple interest?

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(4) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(6) 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.

(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(10) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.