Simple Interest
Math MCQs

Question :    Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

Correct Answer  $7425

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 5%

Time (t) = 7 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) = $5500 × 5% × 7

= $5500 ×⁵/₁₀₀ × 7

= ^{5500 × 5 × 7}/₁₀₀

= ^{27500 × 7}/₁₀₀

= ¹⁹²⁵⁰⁰/₁₀₀

= $1925

Thus, Simple Interest = $1925

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 = $5500 + $1925

= $7425

Thus, Amount to be paid = $7425 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 = $5500

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5500 + ($5500 × 5% × 7)

= $5500 + ($5500 ×⁵/₁₀₀ × 7)

= $5500 + (^{5500 × 5 × 7}/₁₀₀)

= $5500 + (^{27500 × 7}/₁₀₀)

= $5500 + (¹⁹²⁵⁰⁰/₁₀₀)

= $5500 + $1925 = $7425

Thus, Amount (A) to be paid = $7425 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 $5500, the simple interest in 1 year

= ⁵/₁₀₀ × 5500

= ^{5 × 5500}/₁₀₀

= ²⁷⁵⁰⁰/₁₀₀ = $275

Thus, simple interest for 1 year = $275

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $275 × 7 = $1925

Thus, Simple Interest (SI) = $1925

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $1925

= $7425

Thus, Amount to be paid = $7425 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(5) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(8) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?