Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

Correct Answer  $10450

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 9% × 10

= $5500 ×⁹/₁₀₀ × 10

= ^{5500 × 9 × 10}/₁₀₀

= ^{49500 × 10}/₁₀₀

= ⁴⁹⁵⁰⁰⁰/₁₀₀

= $4950

Thus, Simple Interest = $4950

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 + $4950

= $10450

Thus, Amount to be paid = $10450 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) = 10 years

Thus, Amount (A)

= $5500 + ($5500 × 9% × 10)

= $5500 + ($5500 ×⁹/₁₀₀ × 10)

= $5500 + (^{5500 × 9 × 10}/₁₀₀)

= $5500 + (^{49500 × 10}/₁₀₀)

= $5500 + (⁴⁹⁵⁰⁰⁰/₁₀₀)

= $5500 + $4950 = $10450

Thus, Amount (A) to be paid = $10450 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 10 years

= Simple interest for 1 year × 10

= $495 × 10 = $4950

Thus, Simple Interest (SI) = $4950

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $4950

= $10450

Thus, Amount to be paid = $10450 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(8) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?