Simple Interest
Math MCQs

Question :    Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

Correct Answer  $9270

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 10%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8

= $5150 ×¹⁰/₁₀₀ × 8

= ^{5150 × 10 × 8}/₁₀₀

= ^{51500 × 8}/₁₀₀

= ⁴¹²⁰⁰⁰/₁₀₀

= $4120

Thus, Simple Interest = $4120

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 + $4120

= $9270

Thus, Amount to be paid = $9270 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) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5150 + ($5150 × 10% × 8)

= $5150 + ($5150 ×¹⁰/₁₀₀ × 8)

= $5150 + (^{5150 × 10 × 8}/₁₀₀)

= $5150 + (^{51500 × 8}/₁₀₀)

= $5150 + (⁴¹²⁰⁰⁰/₁₀₀)

= $5150 + $4120 = $9270

Thus, Amount (A) to be paid = $9270 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5150

= ^{10 × 5150}/₁₀₀

= ⁵¹⁵⁰⁰/₁₀₀ = $515

Thus, simple interest for 1 year = $515

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $515 × 8 = $4120

Thus, Simple Interest (SI) = $4120

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $4120

= $9270

Thus, Amount to be paid = $9270 Answer

Similar Questions

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

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(8) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.

(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.