Simple Interest
Math MCQs

Question :    What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?

Correct Answer  $5040

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 10%

Time (t) = 6 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) = $3150 × 10% × 6

= $3150 ×¹⁰/₁₀₀ × 6

= ^{3150 × 10 × 6}/₁₀₀

= ^{31500 × 6}/₁₀₀

= ¹⁸⁹⁰⁰⁰/₁₀₀

= $1890

Thus, Simple Interest = $1890

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 + $1890

= $5040

Thus, Amount to be paid = $5040 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) = 10%

And, Time (t) = 6 years

Thus, Amount (A)

= $3150 + ($3150 × 10% × 6)

= $3150 + ($3150 ×¹⁰/₁₀₀ × 6)

= $3150 + (^{3150 × 10 × 6}/₁₀₀)

= $3150 + (^{31500 × 6}/₁₀₀)

= $3150 + (¹⁸⁹⁰⁰⁰/₁₀₀)

= $3150 + $1890 = $5040

Thus, Amount (A) to be paid = $5040 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 $3150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 3150

= ^{10 × 3150}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = $315

Thus, simple interest for 1 year = $315

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $315 × 6 = $1890

Thus, Simple Interest (SI) = $1890

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1890

= $5040

Thus, Amount to be paid = $5040 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(3) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(9) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.