Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

Correct Answer  $9050

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 9%

Time (t) = 9 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) = $5000 × 9% × 9

= $5000 ×⁹/₁₀₀ × 9

= ^{5000 × 9 × 9}/₁₀₀

= ^{45000 × 9}/₁₀₀

= ⁴⁰⁵⁰⁰⁰/₁₀₀

= $4050

Thus, Simple Interest = $4050

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 = $5000 + $4050

= $9050

Thus, Amount to be paid = $9050 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 = $5000

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5000 + ($5000 × 9% × 9)

= $5000 + ($5000 ×⁹/₁₀₀ × 9)

= $5000 + (^{5000 × 9 × 9}/₁₀₀)

= $5000 + (^{45000 × 9}/₁₀₀)

= $5000 + (⁴⁰⁵⁰⁰⁰/₁₀₀)

= $5000 + $4050 = $9050

Thus, Amount (A) to be paid = $9050 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 $5000, the simple interest in 1 year

= ⁹/₁₀₀ × 5000

= ^{9 × 5000}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = $450

Thus, simple interest for 1 year = $450

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $450 × 9 = $4050

Thus, Simple Interest (SI) = $4050

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $4050

= $9050

Thus, Amount to be paid = $9050 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

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

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.