Simple Interest
Math MCQs

Question :    Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

Correct Answer  $9265

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 10%

Time (t) = 7 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% × 7

= $5450 ×¹⁰/₁₀₀ × 7

= ^{5450 × 10 × 7}/₁₀₀

= ^{54500 × 7}/₁₀₀

= ³⁸¹⁵⁰⁰/₁₀₀

= $3815

Thus, Simple Interest = $3815

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 + $3815

= $9265

Thus, Amount to be paid = $9265 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) = 7 years

Thus, Amount (A)

= $5450 + ($5450 × 10% × 7)

= $5450 + ($5450 ×¹⁰/₁₀₀ × 7)

= $5450 + (^{5450 × 10 × 7}/₁₀₀)

= $5450 + (^{54500 × 7}/₁₀₀)

= $5450 + (³⁸¹⁵⁰⁰/₁₀₀)

= $5450 + $3815 = $9265

Thus, Amount (A) to be paid = $9265 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 7 years

= Simple interest for 1 year × 7

= $545 × 7 = $3815

Thus, Simple Interest (SI) = $3815

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $3815

= $9265

Thus, Amount to be paid = $9265 Answer

Similar Questions

(1) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.