Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

Correct Answer  $9000

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 5%

Time (t) = 10 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) = $6000 × 5% × 10

= $6000 ×⁵/₁₀₀ × 10

= ^{6000 × 5 × 10}/₁₀₀

= ^{30000 × 10}/₁₀₀

= ³⁰⁰⁰⁰⁰/₁₀₀

= $3000

Thus, Simple Interest = $3000

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 + $3000

= $9000

Thus, Amount to be paid = $9000 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) = 5%

And, Time (t) = 10 years

Thus, Amount (A)

= $6000 + ($6000 × 5% × 10)

= $6000 + ($6000 ×⁵/₁₀₀ × 10)

= $6000 + (^{6000 × 5 × 10}/₁₀₀)

= $6000 + (^{30000 × 10}/₁₀₀)

= $6000 + (³⁰⁰⁰⁰⁰/₁₀₀)

= $6000 + $3000 = $9000

Thus, Amount (A) to be paid = $9000 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 $6000, the simple interest in 1 year

= ⁵/₁₀₀ × 6000

= ^{5 × 6000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = $300

Thus, simple interest for 1 year = $300

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $300 × 10 = $3000

Thus, Simple Interest (SI) = $3000

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $3000

= $9000

Thus, Amount to be paid = $9000 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(8) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.