Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 3%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5500 × 3% × 10

= $5500 ׳/₁₀₀ × 10

= ^{5500 × 3 × 10}/₁₀₀

= ^{16500 × 10}/₁₀₀

= ¹⁶⁵⁰⁰⁰/₁₀₀

= $1650

Thus, Simple Interest = $1650

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 = $5500 + $1650

= $7150

Thus, Amount to be paid = $7150 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 = $5500

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 10 years

Thus, Amount (A)

= $5500 + ($5500 × 3% × 10)

= $5500 + ($5500 ׳/₁₀₀ × 10)

= $5500 + (^{5500 × 3 × 10}/₁₀₀)

= $5500 + (^{16500 × 10}/₁₀₀)

= $5500 + (¹⁶⁵⁰⁰⁰/₁₀₀)

= $5500 + $1650 = $7150

Thus, Amount (A) to be paid = $7150 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5500, the simple interest in 1 year

= ³/₁₀₀ × 5500

= ^{3 × 5500}/₁₀₀

= ¹⁶⁵⁰⁰/₁₀₀ = $165

Thus, simple interest for 1 year = $165

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $165 × 10 = $1650

Thus, Simple Interest (SI) = $1650

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $1650

= $7150

Thus, Amount to be paid = $7150 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.

(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.