Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

Correct Answer  $7931

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 6%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9

= $5150 ×⁶/₁₀₀ × 9

= ^{5150 × 6 × 9}/₁₀₀

= ^{30900 × 9}/₁₀₀

= ²⁷⁸¹⁰⁰/₁₀₀

= $2781

Thus, Simple Interest = $2781

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 + $2781

= $7931

Thus, Amount to be paid = $7931 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) = 6%

And, Time (t) = 9 years

Thus, Amount (A)

= $5150 + ($5150 × 6% × 9)

= $5150 + ($5150 ×⁶/₁₀₀ × 9)

= $5150 + (^{5150 × 6 × 9}/₁₀₀)

= $5150 + (^{30900 × 9}/₁₀₀)

= $5150 + (²⁷⁸¹⁰⁰/₁₀₀)

= $5150 + $2781 = $7931

Thus, Amount (A) to be paid = $7931 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5150, the simple interest in 1 year

= ⁶/₁₀₀ × 5150

= ^{6 × 5150}/₁₀₀

= ³⁰⁹⁰⁰/₁₀₀ = $309

Thus, simple interest for 1 year = $309

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $309 × 9 = $2781

Thus, Simple Interest (SI) = $2781

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $2781

= $7931

Thus, Amount to be paid = $7931 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(9) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?