Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

Correct Answer  $8250

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 5% × 10

= $5500 ×⁵/₁₀₀ × 10

= ^{5500 × 5 × 10}/₁₀₀

= ^{27500 × 10}/₁₀₀

= ²⁷⁵⁰⁰⁰/₁₀₀

= $2750

Thus, Simple Interest = $2750

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 + $2750

= $8250

Thus, Amount to be paid = $8250 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) = 5%

And, Time (t) = 10 years

Thus, Amount (A)

= $5500 + ($5500 × 5% × 10)

= $5500 + ($5500 ×⁵/₁₀₀ × 10)

= $5500 + (^{5500 × 5 × 10}/₁₀₀)

= $5500 + (^{27500 × 10}/₁₀₀)

= $5500 + (²⁷⁵⁰⁰⁰/₁₀₀)

= $5500 + $2750 = $8250

Thus, Amount (A) to be paid = $8250 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 $5500, the simple interest in 1 year

= ⁵/₁₀₀ × 5500

= ^{5 × 5500}/₁₀₀

= ²⁷⁵⁰⁰/₁₀₀ = $275

Thus, simple interest for 1 year = $275

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $275 × 10 = $2750

Thus, Simple Interest (SI) = $2750

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2750

= $8250

Thus, Amount to be paid = $8250 Answer

Similar Questions

(1) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(5) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(10) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.