Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

Correct Answer  $11400

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 9%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $6000 × 9% × 10

= $6000 ×⁹/₁₀₀ × 10

= ^{6000 × 9 × 10}/₁₀₀

= ^{54000 × 10}/₁₀₀

= ⁵⁴⁰⁰⁰⁰/₁₀₀

= $5400

Thus, Simple Interest = $5400

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 = $6000 + $5400

= $11400

Thus, Amount to be paid = $11400 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 = $6000

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $6000 + ($6000 × 9% × 10)

= $6000 + ($6000 ×⁹/₁₀₀ × 10)

= $6000 + (^{6000 × 9 × 10}/₁₀₀)

= $6000 + (^{54000 × 10}/₁₀₀)

= $6000 + (⁵⁴⁰⁰⁰⁰/₁₀₀)

= $6000 + $5400 = $11400

Thus, Amount (A) to be paid = $11400 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $6000, the simple interest in 1 year

= ⁹/₁₀₀ × 6000

= ^{9 × 6000}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = $540

Thus, simple interest for 1 year = $540

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $540 × 10 = $5400

Thus, Simple Interest (SI) = $5400

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $5400

= $11400

Thus, Amount to be paid = $11400 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(2) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.

(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(6) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(9) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.