Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

Correct Answer  $4284

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 9%

Time (t) = 4 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) = $3150 × 9% × 4

= $3150 ×⁹/₁₀₀ × 4

= ^{3150 × 9 × 4}/₁₀₀

= ^{28350 × 4}/₁₀₀

= ¹¹³⁴⁰⁰/₁₀₀

= $1134

Thus, Simple Interest = $1134

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 = $3150 + $1134

= $4284

Thus, Amount to be paid = $4284 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 = $3150

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 4 years

Thus, Amount (A)

= $3150 + ($3150 × 9% × 4)

= $3150 + ($3150 ×⁹/₁₀₀ × 4)

= $3150 + (^{3150 × 9 × 4}/₁₀₀)

= $3150 + (^{28350 × 4}/₁₀₀)

= $3150 + (¹¹³⁴⁰⁰/₁₀₀)

= $3150 + $1134 = $4284

Thus, Amount (A) to be paid = $4284 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 $3150, the simple interest in 1 year

= ⁹/₁₀₀ × 3150

= ^{9 × 3150}/₁₀₀

= ²⁸³⁵⁰/₁₀₀ = $283.5

Thus, simple interest for 1 year = $283.5

Therefore, simple interest for 4 years

= Simple interest for 1 year × 4

= $283.5 × 4 = $1134

Thus, Simple Interest (SI) = $1134

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1134

= $4284

Thus, Amount to be paid = $4284 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(4) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(6) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?

(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.