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) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.

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

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.