Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7172

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 = $7172 – $4400 = $2772

Thus, Simple Interest = $2772

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 × 2772}/_{4400 × 9}

= ²⁷⁷²⁰⁰/₃₉₆₀₀

= 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) = $4400

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2772 (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 = 9% of Principal

= 9% of $4400

= ⁹/₁₀₀ × 4400

= ^{9 × 4400}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $2772, then the time = ¹/₃₉₆ × 2772 years

= ^{1 × 2772}/₃₉₆ years

= ²⁷⁷²/₃₉₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.

(3) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.

(9) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.