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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(8) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?