Simple Interest
Math MCQs

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

Correct Answer  $10450

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 10%

Time (t) = 9 years

Thus, Amount (A) = ?

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

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

= $5500 ×¹⁰/₁₀₀ × 9

= ^{5500 × 10 × 9}/₁₀₀

= ^{55000 × 9}/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) = 10%

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 10% × 9)

= $5500 + ($5500 ×¹⁰/₁₀₀ × 9)

= $5500 + (^{5500 × 10 × 9}/₁₀₀)

= $5500 + (^{55000 × 9}/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 = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5500, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5500

= ^{10 × 5500}/₁₀₀

= ⁵⁵⁰⁰⁰/₁₀₀ = $550

Thus, simple interest for 1 year = $550

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $550 × 9 = $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) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(4) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.