Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

Correct Answer  $11900

Solution & Explanation

Solution

Given,

Principal (P) = $5950

Rate of Simple Interest (SI) = 10%

Time (t) = 10 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) = $5950 × 10% × 10

= $5950 ×¹⁰/₁₀₀ × 10

= ^{5950 × 10 × 10}/₁₀₀

= ^{59500 × 10}/₁₀₀

= ⁵⁹⁵⁰⁰⁰/₁₀₀

= $5950

Thus, Simple Interest = $5950

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 = $5950 + $5950

= $11900

Thus, Amount to be paid = $11900 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 = $5950

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 10 years

Thus, Amount (A)

= $5950 + ($5950 × 10% × 10)

= $5950 + ($5950 ×¹⁰/₁₀₀ × 10)

= $5950 + (^{5950 × 10 × 10}/₁₀₀)

= $5950 + (^{59500 × 10}/₁₀₀)

= $5950 + (⁵⁹⁵⁰⁰⁰/₁₀₀)

= $5950 + $5950 = $11900

Thus, Amount (A) to be paid = $11900 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 $5950, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5950

= ^{10 × 5950}/₁₀₀

= ⁵⁹⁵⁰⁰/₁₀₀ = $595

Thus, simple interest for 1 year = $595

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $595 × 10 = $5950

Thus, Simple Interest (SI) = $5950

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $5950

= $11900

Thus, Amount to be paid = $11900 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.

(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

(10) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.