Simple Interest
Math MCQs

Question :    Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.

Correct Answer  $8493

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 7%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7

= $5700 ×⁷/₁₀₀ × 7

= ^{5700 × 7 × 7}/₁₀₀

= ^{39900 × 7}/₁₀₀

= ²⁷⁹³⁰⁰/₁₀₀

= $2793

Thus, Simple Interest = $2793

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 + $2793

= $8493

Thus, Amount to be paid = $8493 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) = 7%

And, Time (t) = 7 years

Thus, Amount (A)

= $5700 + ($5700 × 7% × 7)

= $5700 + ($5700 ×⁷/₁₀₀ × 7)

= $5700 + (^{5700 × 7 × 7}/₁₀₀)

= $5700 + (^{39900 × 7}/₁₀₀)

= $5700 + (²⁷⁹³⁰⁰/₁₀₀)

= $5700 + $2793 = $8493

Thus, Amount (A) to be paid = $8493 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5700, the simple interest in 1 year

= ⁷/₁₀₀ × 5700

= ^{7 × 5700}/₁₀₀

= ³⁹⁹⁰⁰/₁₀₀ = $399

Thus, simple interest for 1 year = $399

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $399 × 7 = $2793

Thus, Simple Interest (SI) = $2793

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $2793

= $8493

Thus, Amount to be paid = $8493 Answer

Similar Questions

(1) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(2) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(9) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.