Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

Correct Answer  $9690

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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) = $5100 × 10% × 9

= $5100 ×¹⁰/₁₀₀ × 9

= ^{5100 × 10 × 9}/₁₀₀

= ^{51000 × 9}/₁₀₀

= ⁴⁵⁹⁰⁰⁰/₁₀₀

= $4590

Thus, Simple Interest = $4590

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 + $4590

= $9690

Thus, Amount to be paid = $9690 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) = 10%

And, Time (t) = 9 years

Thus, Amount (A)

= $5100 + ($5100 × 10% × 9)

= $5100 + ($5100 ×¹⁰/₁₀₀ × 9)

= $5100 + (^{5100 × 10 × 9}/₁₀₀)

= $5100 + (^{51000 × 9}/₁₀₀)

= $5100 + (⁴⁵⁹⁰⁰⁰/₁₀₀)

= $5100 + $4590 = $9690

Thus, Amount (A) to be paid = $9690 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 $5100, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = $510

Thus, simple interest for 1 year = $510

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $510 × 9 = $4590

Thus, Simple Interest (SI) = $4590

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5100 + $4590

= $9690

Thus, Amount to be paid = $9690 Answer

Similar Questions

(1) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(5) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.

(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.