Simple Interest
Math MCQs

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

Correct Answer  $9690

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (SI) = 9%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10

= $5100 ×⁹/₁₀₀ × 10

= ^{5100 × 9 × 10}/₁₀₀

= ^{45900 × 10}/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) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5100 + ($5100 × 9% × 10)

= $5100 + ($5100 ×⁹/₁₀₀ × 10)

= $5100 + (^{5100 × 9 × 10}/₁₀₀)

= $5100 + (^{45900 × 10}/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 = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5100, the simple interest in 1 year

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = $459

Thus, simple interest for 1 year = $459

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $459 × 10 = $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) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(2) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?