Simple Interest
Math MCQs

Question :    Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

Correct Answer  $7194

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 4%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5450 × 4% × 8

= $5450 ×⁴/₁₀₀ × 8

= ^{5450 × 4 × 8}/₁₀₀

= ^{21800 × 8}/₁₀₀

= ¹⁷⁴⁴⁰⁰/₁₀₀

= $1744

Thus, Simple Interest = $1744

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 = $5450 + $1744

= $7194

Thus, Amount to be paid = $7194 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 = $5450

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 8 years

Thus, Amount (A)

= $5450 + ($5450 × 4% × 8)

= $5450 + ($5450 ×⁴/₁₀₀ × 8)

= $5450 + (^{5450 × 4 × 8}/₁₀₀)

= $5450 + (^{21800 × 8}/₁₀₀)

= $5450 + (¹⁷⁴⁴⁰⁰/₁₀₀)

= $5450 + $1744 = $7194

Thus, Amount (A) to be paid = $7194 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $5450, the simple interest in 1 year

= ⁴/₁₀₀ × 5450

= ^{4 × 5450}/₁₀₀

= ²¹⁸⁰⁰/₁₀₀ = $218

Thus, simple interest for 1 year = $218

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $218 × 8 = $1744

Thus, Simple Interest (SI) = $1744

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $1744

= $7194

Thus, Amount to be paid = $7194 Answer

Similar Questions

(1) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(6) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(10) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.