Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

Correct Answer  $9955

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 9% × 9

= $5500 ×⁹/₁₀₀ × 9

= ^{5500 × 9 × 9}/₁₀₀

= ^{49500 × 9}/₁₀₀

= ⁴⁴⁵⁵⁰⁰/₁₀₀

= $4455

Thus, Simple Interest = $4455

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 = $5500 + $4455

= $9955

Thus, Amount to be paid = $9955 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 = $5500

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 9% × 9)

= $5500 + ($5500 ×⁹/₁₀₀ × 9)

= $5500 + (^{5500 × 9 × 9}/₁₀₀)

= $5500 + (^{49500 × 9}/₁₀₀)

= $5500 + (⁴⁴⁵⁵⁰⁰/₁₀₀)

= $5500 + $4455 = $9955

Thus, Amount (A) to be paid = $9955 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 $5500, the simple interest in 1 year

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = $495

Thus, simple interest for 1 year = $495

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $495 × 9 = $4455

Thus, Simple Interest (SI) = $4455

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $4455

= $9955

Thus, Amount to be paid = $9955 Answer

Similar Questions

(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(4) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?