Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

Correct Answer  $6962

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 2%

Time (t) = 9 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) = $5900 × 2% × 9

= $5900 ײ/₁₀₀ × 9

= ^{5900 × 2 × 9}/₁₀₀

= ^{11800 × 9}/₁₀₀

= ¹⁰⁶²⁰⁰/₁₀₀

= $1062

Thus, Simple Interest = $1062

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 = $5900 + $1062

= $6962

Thus, Amount to be paid = $6962 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 = $5900

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5900 + ($5900 × 2% × 9)

= $5900 + ($5900 ײ/₁₀₀ × 9)

= $5900 + (^{5900 × 2 × 9}/₁₀₀)

= $5900 + (^{11800 × 9}/₁₀₀)

= $5900 + (¹⁰⁶²⁰⁰/₁₀₀)

= $5900 + $1062 = $6962

Thus, Amount (A) to be paid = $6962 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 $5900, the simple interest in 1 year

= ²/₁₀₀ × 5900

= ^{2 × 5900}/₁₀₀

= ¹¹⁸⁰⁰/₁₀₀ = $118

Thus, simple interest for 1 year = $118

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $118 × 9 = $1062

Thus, Simple Interest (SI) = $1062

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $1062

= $6962

Thus, Amount to be paid = $6962 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.

(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(7) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?

(9) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.