Simple Interest
Math MCQs

Question :    Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

Correct Answer  $10148

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 9%

Time (t) = 8 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) = $5900 × 9% × 8

= $5900 ×⁹/₁₀₀ × 8

= ^{5900 × 9 × 8}/₁₀₀

= ^{53100 × 8}/₁₀₀

= ⁴²⁴⁸⁰⁰/₁₀₀

= $4248

Thus, Simple Interest = $4248

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 + $4248

= $10148

Thus, Amount to be paid = $10148 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) = 9%

And, Time (t) = 8 years

Thus, Amount (A)

= $5900 + ($5900 × 9% × 8)

= $5900 + ($5900 ×⁹/₁₀₀ × 8)

= $5900 + (^{5900 × 9 × 8}/₁₀₀)

= $5900 + (^{53100 × 8}/₁₀₀)

= $5900 + (⁴²⁴⁸⁰⁰/₁₀₀)

= $5900 + $4248 = $10148

Thus, Amount (A) to be paid = $10148 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 $5900, the simple interest in 1 year

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = $531

Thus, simple interest for 1 year = $531

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $531 × 8 = $4248

Thus, Simple Interest (SI) = $4248

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $4248

= $10148

Thus, Amount to be paid = $10148 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(6) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.