Simple Interest
Math MCQs

Question :    Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

Correct Answer  $6594.5

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 3%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7

= $5450 ׳/₁₀₀ × 7

= ^{5450 × 3 × 7}/₁₀₀

= ^{16350 × 7}/₁₀₀

= ¹¹⁴⁴⁵⁰/₁₀₀

= $1144.5

Thus, Simple Interest = $1144.5

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 + $1144.5

= $6594.5

Thus, Amount to be paid = $6594.5 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) = 3%

And, Time (t) = 7 years

Thus, Amount (A)

= $5450 + ($5450 × 3% × 7)

= $5450 + ($5450 ׳/₁₀₀ × 7)

= $5450 + (^{5450 × 3 × 7}/₁₀₀)

= $5450 + (^{16350 × 7}/₁₀₀)

= $5450 + (¹¹⁴⁴⁵⁰/₁₀₀)

= $5450 + $1144.5 = $6594.5

Thus, Amount (A) to be paid = $6594.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5450, the simple interest in 1 year

= ³/₁₀₀ × 5450

= ^{3 × 5450}/₁₀₀

= ¹⁶³⁵⁰/₁₀₀ = $163.5

Thus, simple interest for 1 year = $163.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $163.5 × 7 = $1144.5

Thus, Simple Interest (SI) = $1144.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $1144.5

= $6594.5

Thus, Amount to be paid = $6594.5 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(4) 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?

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(6) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.

(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(9) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.