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 $7480 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) = 10% per annum

Amount (A) = $7480

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 = $7480 – $4400 = $3080

Thus, Simple Interest = $3080

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 × 3080}/_{4400 × 10}

= ³⁰⁸⁰⁰⁰/₄₄₀₀₀

= 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) = 10% per annum

Simple Interest = $3080 (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 $3080, then the time = ¹/₄₄₀ × 3080 years

= ^{1 × 3080}/₄₄₀ years

= ³⁰⁸⁰/₄₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.

(2) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(10) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.