Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

Correct Answer  $4095

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 10%

Time (t) = 3 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $3150 × 10% × 3

= $3150 ×¹⁰/₁₀₀ × 3

= ^{3150 × 10 × 3}/₁₀₀

= ^{31500 × 3}/₁₀₀

= ⁹⁴⁵⁰⁰/₁₀₀

= $945

Thus, Simple Interest = $945

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $945

= $4095

Thus, Amount to be paid = $4095 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $3150

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 3 years

Thus, Amount (A)

= $3150 + ($3150 × 10% × 3)

= $3150 + ($3150 ×¹⁰/₁₀₀ × 3)

= $3150 + (^{3150 × 10 × 3}/₁₀₀)

= $3150 + (^{31500 × 3}/₁₀₀)

= $3150 + (⁹⁴⁵⁰⁰/₁₀₀)

= $3150 + $945 = $4095

Thus, Amount (A) to be paid = $4095 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $3150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3150

= ^{10 × 3150}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = $315

Thus, simple interest for 1 year = $315

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $315 × 3 = $945

Thus, Simple Interest (SI) = $945

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $945

= $4095

Thus, Amount to be paid = $4095 Answer

Similar Questions

(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(3) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.

(4) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(8) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.