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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(2) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(3) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(9) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.