Simple Interest
Math MCQs

Question :    Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.

Correct Answer  $4278

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 8%

Time (t) = 3 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3450 × 8% × 3

= $3450 ×⁸/₁₀₀ × 3

= ^{3450 × 8 × 3}/₁₀₀

= ^{27600 × 3}/₁₀₀

= ⁸²⁸⁰⁰/₁₀₀

= $828

Thus, Simple Interest = $828

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 = $3450 + $828

= $4278

Thus, Amount to be paid = $4278 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 = $3450

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 3 years

Thus, Amount (A)

= $3450 + ($3450 × 8% × 3)

= $3450 + ($3450 ×⁸/₁₀₀ × 3)

= $3450 + (^{3450 × 8 × 3}/₁₀₀)

= $3450 + (^{27600 × 3}/₁₀₀)

= $3450 + (⁸²⁸⁰⁰/₁₀₀)

= $3450 + $828 = $4278

Thus, Amount (A) to be paid = $4278 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $3450, the simple interest in 1 year

= ⁸/₁₀₀ × 3450

= ^{8 × 3450}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = $276

Thus, simple interest for 1 year = $276

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $276 × 3 = $828

Thus, Simple Interest (SI) = $828

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $828

= $4278

Thus, Amount to be paid = $4278 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(3) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.