Simple Interest
Math MCQs

Question :    Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

Correct Answer  $7599

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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) = $5100 × 7% × 7

= $5100 ×⁷/₁₀₀ × 7

= ^{5100 × 7 × 7}/₁₀₀

= ^{35700 × 7}/₁₀₀

= ²⁴⁹⁹⁰⁰/₁₀₀

= $2499

Thus, Simple Interest = $2499

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 = $5100 + $2499

= $7599

Thus, Amount to be paid = $7599 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 = $5100

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 7 years

Thus, Amount (A)

= $5100 + ($5100 × 7% × 7)

= $5100 + ($5100 ×⁷/₁₀₀ × 7)

= $5100 + (^{5100 × 7 × 7}/₁₀₀)

= $5100 + (^{35700 × 7}/₁₀₀)

= $5100 + (²⁴⁹⁹⁰⁰/₁₀₀)

= $5100 + $2499 = $7599

Thus, Amount (A) to be paid = $7599 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 $5100, the simple interest in 1 year

= ⁷/₁₀₀ × 5100

= ^{7 × 5100}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = $357

Thus, simple interest for 1 year = $357

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $357 × 7 = $2499

Thus, Simple Interest (SI) = $2499

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5100 + $2499

= $7599

Thus, Amount to be paid = $7599 Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(7) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

(9) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?

(10) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.