Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

Correct Answer  $9594

Solution & Explanation

Solution

Given,

Principal (P) = $5850

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) = $5850 × 8% × 8

= $5850 ×⁸/₁₀₀ × 8

= ^{5850 × 8 × 8}/₁₀₀

= ^{46800 × 8}/₁₀₀

= ³⁷⁴⁴⁰⁰/₁₀₀

= $3744

Thus, Simple Interest = $3744

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 = $5850 + $3744

= $9594

Thus, Amount to be paid = $9594 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 = $5850

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 8 years

Thus, Amount (A)

= $5850 + ($5850 × 8% × 8)

= $5850 + ($5850 ×⁸/₁₀₀ × 8)

= $5850 + (^{5850 × 8 × 8}/₁₀₀)

= $5850 + (^{46800 × 8}/₁₀₀)

= $5850 + (³⁷⁴⁴⁰⁰/₁₀₀)

= $5850 + $3744 = $9594

Thus, Amount (A) to be paid = $9594 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 $5850, the simple interest in 1 year

= ⁸/₁₀₀ × 5850

= ^{8 × 5850}/₁₀₀

= ⁴⁶⁸⁰⁰/₁₀₀ = $468

Thus, simple interest for 1 year = $468

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $468 × 8 = $3744

Thus, Simple Interest (SI) = $3744

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $3744

= $9594

Thus, Amount to be paid = $9594 Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?

(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(6) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.

(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(10) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.