Simple Interest
Math MCQs

Question :    Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.

Correct Answer  $7739

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 6%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7

= $5450 ×⁶/₁₀₀ × 7

= ^{5450 × 6 × 7}/₁₀₀

= ^{32700 × 7}/₁₀₀

= ²²⁸⁹⁰⁰/₁₀₀

= $2289

Thus, Simple Interest = $2289

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 + $2289

= $7739

Thus, Amount to be paid = $7739 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) = 6%

And, Time (t) = 7 years

Thus, Amount (A)

= $5450 + ($5450 × 6% × 7)

= $5450 + ($5450 ×⁶/₁₀₀ × 7)

= $5450 + (^{5450 × 6 × 7}/₁₀₀)

= $5450 + (^{32700 × 7}/₁₀₀)

= $5450 + (²²⁸⁹⁰⁰/₁₀₀)

= $5450 + $2289 = $7739

Thus, Amount (A) to be paid = $7739 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5450, the simple interest in 1 year

= ⁶/₁₀₀ × 5450

= ^{6 × 5450}/₁₀₀

= ³²⁷⁰⁰/₁₀₀ = $327

Thus, simple interest for 1 year = $327

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $327 × 7 = $2289

Thus, Simple Interest (SI) = $2289

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $2289

= $7739

Thus, Amount to be paid = $7739 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(2) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

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

(9) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.