Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

Correct Answer  $6018

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (SI) = 2%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9

= $5100 ײ/₁₀₀ × 9

= ^{5100 × 2 × 9}/₁₀₀

= ^{10200 × 9}/₁₀₀

= ⁹¹⁸⁰⁰/₁₀₀

= $918

Thus, Simple Interest = $918

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 + $918

= $6018

Thus, Amount to be paid = $6018 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) = 2%

And, Time (t) = 9 years

Thus, Amount (A)

= $5100 + ($5100 × 2% × 9)

= $5100 + ($5100 ײ/₁₀₀ × 9)

= $5100 + (^{5100 × 2 × 9}/₁₀₀)

= $5100 + (^{10200 × 9}/₁₀₀)

= $5100 + (⁹¹⁸⁰⁰/₁₀₀)

= $5100 + $918 = $6018

Thus, Amount (A) to be paid = $6018 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5100, the simple interest in 1 year

= ²/₁₀₀ × 5100

= ^{2 × 5100}/₁₀₀

= ¹⁰²⁰⁰/₁₀₀ = $102

Thus, simple interest for 1 year = $102

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $102 × 9 = $918

Thus, Simple Interest (SI) = $918

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5100 + $918

= $6018

Thus, Amount to be paid = $6018 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(2) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(6) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(9) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.