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) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(5) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?

(7) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.