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) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(3) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(4) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

(10) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.