Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

Correct Answer  $6060

Solution & Explanation

Solution

Given,

Principal (P) = $5050

Rate of Simple Interest (SI) = 2%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5050 × 2% × 10

= $5050 ײ/₁₀₀ × 10

= ^{5050 × 2 × 10}/₁₀₀

= ^{10100 × 10}/₁₀₀

= ¹⁰¹⁰⁰⁰/₁₀₀

= $1010

Thus, Simple Interest = $1010

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 = $5050 + $1010

= $6060

Thus, Amount to be paid = $6060 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 = $5050

Rate of Simple Interest (SI) or (R) = 2%

And, Time (t) = 10 years

Thus, Amount (A)

= $5050 + ($5050 × 2% × 10)

= $5050 + ($5050 ײ/₁₀₀ × 10)

= $5050 + (^{5050 × 2 × 10}/₁₀₀)

= $5050 + (^{10100 × 10}/₁₀₀)

= $5050 + (¹⁰¹⁰⁰⁰/₁₀₀)

= $5050 + $1010 = $6060

Thus, Amount (A) to be paid = $6060 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5050, the simple interest in 1 year

= ²/₁₀₀ × 5050

= ^{2 × 5050}/₁₀₀

= ¹⁰¹⁰⁰/₁₀₀ = $101

Thus, simple interest for 1 year = $101

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $101 × 10 = $1010

Thus, Simple Interest (SI) = $1010

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $1010

= $6060

Thus, Amount to be paid = $6060 Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.

(4) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(9) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.