Simple Interest
Math MCQs

Question :    Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

Correct Answer  $7290

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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) = $5400 × 5% × 7

= $5400 ×⁵/₁₀₀ × 7

= ^{5400 × 5 × 7}/₁₀₀

= ^{27000 × 7}/₁₀₀

= ¹⁸⁹⁰⁰⁰/₁₀₀

= $1890

Thus, Simple Interest = $1890

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 = $5400 + $1890

= $7290

Thus, Amount to be paid = $7290 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 = $5400

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5400 + ($5400 × 5% × 7)

= $5400 + ($5400 ×⁵/₁₀₀ × 7)

= $5400 + (^{5400 × 5 × 7}/₁₀₀)

= $5400 + (^{27000 × 7}/₁₀₀)

= $5400 + (¹⁸⁹⁰⁰⁰/₁₀₀)

= $5400 + $1890 = $7290

Thus, Amount (A) to be paid = $7290 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 $5400, the simple interest in 1 year

= ⁵/₁₀₀ × 5400

= ^{5 × 5400}/₁₀₀

= ²⁷⁰⁰⁰/₁₀₀ = $270

Thus, simple interest for 1 year = $270

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $270 × 7 = $1890

Thus, Simple Interest (SI) = $1890

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5400 + $1890

= $7290

Thus, Amount to be paid = $7290 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.

(2) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?

(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.