Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

Correct Answer  $10260

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (SI) = 9%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5400 × 9% × 10

= $5400 ×⁹/₁₀₀ × 10

= ^{5400 × 9 × 10}/₁₀₀

= ^{48600 × 10}/₁₀₀

= ⁴⁸⁶⁰⁰⁰/₁₀₀

= $4860

Thus, Simple Interest = $4860

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 = $5400 + $4860

= $10260

Thus, Amount to be paid = $10260 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 = $5400

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5400 + ($5400 × 9% × 10)

= $5400 + ($5400 ×⁹/₁₀₀ × 10)

= $5400 + (^{5400 × 9 × 10}/₁₀₀)

= $5400 + (^{48600 × 10}/₁₀₀)

= $5400 + (⁴⁸⁶⁰⁰⁰/₁₀₀)

= $5400 + $4860 = $10260

Thus, Amount (A) to be paid = $10260 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5400, the simple interest in 1 year

= ⁹/₁₀₀ × 5400

= ^{9 × 5400}/₁₀₀

= ⁴⁸⁶⁰⁰/₁₀₀ = $486

Thus, simple interest for 1 year = $486

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $486 × 10 = $4860

Thus, Simple Interest (SI) = $4860

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5400 + $4860

= $10260

Thus, Amount to be paid = $10260 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

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

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

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

(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(8) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.