Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

Correct Answer  $11800

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 10%

Time (t) = 10 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) = $5900 × 10% × 10

= $5900 ×¹⁰/₁₀₀ × 10

= ^{5900 × 10 × 10}/₁₀₀

= ^{59000 × 10}/₁₀₀

= ⁵⁹⁰⁰⁰⁰/₁₀₀

= $5900

Thus, Simple Interest = $5900

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 = $5900 + $5900

= $11800

Thus, Amount to be paid = $11800 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 = $5900

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 10 years

Thus, Amount (A)

= $5900 + ($5900 × 10% × 10)

= $5900 + ($5900 ×¹⁰/₁₀₀ × 10)

= $5900 + (^{5900 × 10 × 10}/₁₀₀)

= $5900 + (^{59000 × 10}/₁₀₀)

= $5900 + (⁵⁹⁰⁰⁰⁰/₁₀₀)

= $5900 + $5900 = $11800

Thus, Amount (A) to be paid = $11800 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 $5900, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5900

= ^{10 × 5900}/₁₀₀

= ⁵⁹⁰⁰⁰/₁₀₀ = $590

Thus, simple interest for 1 year = $590

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $590 × 10 = $5900

Thus, Simple Interest (SI) = $5900

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $5900

= $11800

Thus, Amount to be paid = $11800 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(4) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(5) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?