Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

Correct Answer  $10830

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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) = $5700 × 10% × 9

= $5700 ×¹⁰/₁₀₀ × 9

= ^{5700 × 10 × 9}/₁₀₀

= ^{57000 × 9}/₁₀₀

= ⁵¹³⁰⁰⁰/₁₀₀

= $5130

Thus, Simple Interest = $5130

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 = $5700 + $5130

= $10830

Thus, Amount to be paid = $10830 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 = $5700

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5700 + ($5700 × 10% × 9)

= $5700 + ($5700 ×¹⁰/₁₀₀ × 9)

= $5700 + (^{5700 × 10 × 9}/₁₀₀)

= $5700 + (^{57000 × 9}/₁₀₀)

= $5700 + (⁵¹³⁰⁰⁰/₁₀₀)

= $5700 + $5130 = $10830

Thus, Amount (A) to be paid = $10830 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 $5700, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = $570

Thus, simple interest for 1 year = $570

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $570 × 9 = $5130

Thus, Simple Interest (SI) = $5130

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $5130

= $10830

Thus, Amount to be paid = $10830 Answer

Similar Questions

(1) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.

(8) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.