Simple Interest
Math MCQs

Question :    Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

Correct Answer  $7130

Solution & Explanation

Solution

Given,

Principal (P) = $5750

Rate of Simple Interest (SI) = 3%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5750 × 3% × 8

= $5750 ׳/₁₀₀ × 8

= ^{5750 × 3 × 8}/₁₀₀

= ^{17250 × 8}/₁₀₀

= ¹³⁸⁰⁰⁰/₁₀₀

= $1380

Thus, Simple Interest = $1380

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 = $5750 + $1380

= $7130

Thus, Amount to be paid = $7130 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 = $5750

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 8 years

Thus, Amount (A)

= $5750 + ($5750 × 3% × 8)

= $5750 + ($5750 ׳/₁₀₀ × 8)

= $5750 + (^{5750 × 3 × 8}/₁₀₀)

= $5750 + (^{17250 × 8}/₁₀₀)

= $5750 + (¹³⁸⁰⁰⁰/₁₀₀)

= $5750 + $1380 = $7130

Thus, Amount (A) to be paid = $7130 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5750, the simple interest in 1 year

= ³/₁₀₀ × 5750

= ^{3 × 5750}/₁₀₀

= ¹⁷²⁵⁰/₁₀₀ = $172.5

Thus, simple interest for 1 year = $172.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $172.5 × 8 = $1380

Thus, Simple Interest (SI) = $1380

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $1380

= $7130

Thus, Amount to be paid = $7130 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(2) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(4) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(9) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.