Simple Interest
Math MCQs

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

Correct Answer  $9430

Solution & Explanation

Solution

Given,

Principal (P) = $5750

Rate of Simple Interest (SI) = 8%

Time (t) = 8 years

Thus, Amount (A) = ?

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

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

= $5750 ×⁸/₁₀₀ × 8

= ^{5750 × 8 × 8}/₁₀₀

= ^{46000 × 8}/₁₀₀

= ³⁶⁸⁰⁰⁰/₁₀₀

= $3680

Thus, Simple Interest = $3680

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 + $3680

= $9430

Thus, Amount to be paid = $9430 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) = 8%

And, Time (t) = 8 years

Thus, Amount (A)

= $5750 + ($5750 × 8% × 8)

= $5750 + ($5750 ×⁸/₁₀₀ × 8)

= $5750 + (^{5750 × 8 × 8}/₁₀₀)

= $5750 + (^{46000 × 8}/₁₀₀)

= $5750 + (³⁶⁸⁰⁰⁰/₁₀₀)

= $5750 + $3680 = $9430

Thus, Amount (A) to be paid = $9430 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5750, the simple interest in 1 year

= ⁸/₁₀₀ × 5750

= ^{8 × 5750}/₁₀₀

= ⁴⁶⁰⁰⁰/₁₀₀ = $460

Thus, simple interest for 1 year = $460

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $460 × 8 = $3680

Thus, Simple Interest (SI) = $3680

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $3680

= $9430

Thus, Amount to be paid = $9430 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(10) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?