Simple Interest
Math MCQs

Question :    Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

Correct Answer  $3782

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (SI) = 8%

Time (t) = 3 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3050 × 8% × 3

= $3050 ×⁸/₁₀₀ × 3

= ^{3050 × 8 × 3}/₁₀₀

= ^{24400 × 3}/₁₀₀

= ⁷³²⁰⁰/₁₀₀

= $732

Thus, Simple Interest = $732

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 = $3050 + $732

= $3782

Thus, Amount to be paid = $3782 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 = $3050

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 3 years

Thus, Amount (A)

= $3050 + ($3050 × 8% × 3)

= $3050 + ($3050 ×⁸/₁₀₀ × 3)

= $3050 + (^{3050 × 8 × 3}/₁₀₀)

= $3050 + (^{24400 × 3}/₁₀₀)

= $3050 + (⁷³²⁰⁰/₁₀₀)

= $3050 + $732 = $3782

Thus, Amount (A) to be paid = $3782 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $3050, the simple interest in 1 year

= ⁸/₁₀₀ × 3050

= ^{8 × 3050}/₁₀₀

= ²⁴⁴⁰⁰/₁₀₀ = $244

Thus, simple interest for 1 year = $244

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $244 × 3 = $732

Thus, Simple Interest (SI) = $732

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3050 + $732

= $3782

Thus, Amount to be paid = $3782 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

(2) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.

(7) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?