Simple Interest
Math MCQs

Question :    What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

Correct Answer  $4375

Solution & Explanation

Solution

Given,

Principal (P) = $3500

Rate of Simple Interest (SI) = 5%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $3500 × 5% × 5

= $3500 ×⁵/₁₀₀ × 5

= ^{3500 × 5 × 5}/₁₀₀

= ^{17500 × 5}/₁₀₀

= ⁸⁷⁵⁰⁰/₁₀₀

= $875

Thus, Simple Interest = $875

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 = $3500 + $875

= $4375

Thus, Amount to be paid = $4375 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 = $3500

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 5 years

Thus, Amount (A)

= $3500 + ($3500 × 5% × 5)

= $3500 + ($3500 ×⁵/₁₀₀ × 5)

= $3500 + (^{3500 × 5 × 5}/₁₀₀)

= $3500 + (^{17500 × 5}/₁₀₀)

= $3500 + (⁸⁷⁵⁰⁰/₁₀₀)

= $3500 + $875 = $4375

Thus, Amount (A) to be paid = $4375 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $3500, the simple interest in 1 year

= ⁵/₁₀₀ × 3500

= ^{5 × 3500}/₁₀₀

= ¹⁷⁵⁰⁰/₁₀₀ = $175

Thus, simple interest for 1 year = $175

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $175 × 5 = $875

Thus, Simple Interest (SI) = $875

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3500 + $875

= $4375

Thus, Amount to be paid = $4375 Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?