Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

Correct Answer  $10355

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 10%

Time (t) = 9 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) = $5450 × 10% × 9

= $5450 ×¹⁰/₁₀₀ × 9

= ^{5450 × 10 × 9}/₁₀₀

= ^{54500 × 9}/₁₀₀

= ⁴⁹⁰⁵⁰⁰/₁₀₀

= $4905

Thus, Simple Interest = $4905

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 = $5450 + $4905

= $10355

Thus, Amount to be paid = $10355 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 = $5450

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5450 + ($5450 × 10% × 9)

= $5450 + ($5450 ×¹⁰/₁₀₀ × 9)

= $5450 + (^{5450 × 10 × 9}/₁₀₀)

= $5450 + (^{54500 × 9}/₁₀₀)

= $5450 + (⁴⁹⁰⁵⁰⁰/₁₀₀)

= $5450 + $4905 = $10355

Thus, Amount (A) to be paid = $10355 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 $5450, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5450

= ^{10 × 5450}/₁₀₀

= ⁵⁴⁵⁰⁰/₁₀₀ = $545

Thus, simple interest for 1 year = $545

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $545 × 9 = $4905

Thus, Simple Interest (SI) = $4905

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $4905

= $10355

Thus, Amount to be paid = $10355 Answer

Similar Questions

(1) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(4) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.