Simple Interest
Math MCQs

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

Correct Answer  $10900

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 10%

Time (t) = 10 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% × 10

= $5450 ×¹⁰/₁₀₀ × 10

= ^{5450 × 10 × 10}/₁₀₀

= ^{54500 × 10}/₁₀₀

= ⁵⁴⁵⁰⁰⁰/₁₀₀

= $5450

Thus, Simple Interest = $5450

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 + $5450

= $10900

Thus, Amount to be paid = $10900 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) = 10 years

Thus, Amount (A)

= $5450 + ($5450 × 10% × 10)

= $5450 + ($5450 ×¹⁰/₁₀₀ × 10)

= $5450 + (^{5450 × 10 × 10}/₁₀₀)

= $5450 + (^{54500 × 10}/₁₀₀)

= $5450 + (⁵⁴⁵⁰⁰⁰/₁₀₀)

= $5450 + $5450 = $10900

Thus, Amount (A) to be paid = $10900 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 10 years

= Simple interest for 1 year × 10

= $545 × 10 = $5450

Thus, Simple Interest (SI) = $5450

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $5450

= $10900

Thus, Amount to be paid = $10900 Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(2) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(4) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

(5) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(8) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.