Simple Interest
Math MCQs

Question :    What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

Correct Answer  $5400

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (SI) = 7%

Time (t) = 5 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $4000 × 7% × 5

= $4000 ×⁷/₁₀₀ × 5

= ^{4000 × 7 × 5}/₁₀₀

= ^{28000 × 5}/₁₀₀

= ¹⁴⁰⁰⁰⁰/₁₀₀

= $1400

Thus, Simple Interest = $1400

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 = $4000 + $1400

= $5400

Thus, Amount to be paid = $5400 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 = $4000

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 5 years

Thus, Amount (A)

= $4000 + ($4000 × 7% × 5)

= $4000 + ($4000 ×⁷/₁₀₀ × 5)

= $4000 + (^{4000 × 7 × 5}/₁₀₀)

= $4000 + (^{28000 × 5}/₁₀₀)

= $4000 + (¹⁴⁰⁰⁰⁰/₁₀₀)

= $4000 + $1400 = $5400

Thus, Amount (A) to be paid = $5400 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $4000, the simple interest in 1 year

= ⁷/₁₀₀ × 4000

= ^{7 × 4000}/₁₀₀

= ²⁸⁰⁰⁰/₁₀₀ = $280

Thus, simple interest for 1 year = $280

Therefore, simple interest for 5 years

= Simple interest for 1 year × 5

= $280 × 5 = $1400

Thus, Simple Interest (SI) = $1400

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $4000 + $1400

= $5400

Thus, Amount to be paid = $5400 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(6) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?

(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?