Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

Correct Answer  $11305

Solution & Explanation

Solution

Given,

Principal (P) = $5950

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) = $5950 × 10% × 9

= $5950 ×¹⁰/₁₀₀ × 9

= ^{5950 × 10 × 9}/₁₀₀

= ^{59500 × 9}/₁₀₀

= ⁵³⁵⁵⁰⁰/₁₀₀

= $5355

Thus, Simple Interest = $5355

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 = $5950 + $5355

= $11305

Thus, Amount to be paid = $11305 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 = $5950

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5950 + ($5950 × 10% × 9)

= $5950 + ($5950 ×¹⁰/₁₀₀ × 9)

= $5950 + (^{5950 × 10 × 9}/₁₀₀)

= $5950 + (^{59500 × 9}/₁₀₀)

= $5950 + (⁵³⁵⁵⁰⁰/₁₀₀)

= $5950 + $5355 = $11305

Thus, Amount (A) to be paid = $11305 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 $5950, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5950

= ^{10 × 5950}/₁₀₀

= ⁵⁹⁵⁰⁰/₁₀₀ = $595

Thus, simple interest for 1 year = $595

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $595 × 9 = $5355

Thus, Simple Interest (SI) = $5355

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $5355

= $11305

Thus, Amount to be paid = $11305 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(4) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.