Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

Correct Answer  $6077

Solution & Explanation

Solution

Given,

Principal (P) = $5150

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) = $5150 × 2% × 9

= $5150 ײ/₁₀₀ × 9

= ^{5150 × 2 × 9}/₁₀₀

= ^{10300 × 9}/₁₀₀

= ⁹²⁷⁰⁰/₁₀₀

= $927

Thus, Simple Interest = $927

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 = $5150 + $927

= $6077

Thus, Amount to be paid = $6077 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 = $5150

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5150 + ($5150 × 2% × 9)

= $5150 + ($5150 ײ/₁₀₀ × 9)

= $5150 + (^{5150 × 2 × 9}/₁₀₀)

= $5150 + (^{10300 × 9}/₁₀₀)

= $5150 + (⁹²⁷⁰⁰/₁₀₀)

= $5150 + $927 = $6077

Thus, Amount (A) to be paid = $6077 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 $5150, the simple interest in 1 year

= ²/₁₀₀ × 5150

= ^{2 × 5150}/₁₀₀

= ¹⁰³⁰⁰/₁₀₀ = $103

Thus, simple interest for 1 year = $103

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $103 × 9 = $927

Thus, Simple Interest (SI) = $927

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $927

= $6077

Thus, Amount to be paid = $6077 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(2) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(6) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?