Simple Interest
Math MCQs

Question :    Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

Correct Answer  $9758

Solution & Explanation

Solution

Given,

Principal (P) = $5950

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) = $5950 × 8% × 8

= $5950 ×⁸/₁₀₀ × 8

= ^{5950 × 8 × 8}/₁₀₀

= ^{47600 × 8}/₁₀₀

= ³⁸⁰⁸⁰⁰/₁₀₀

= $3808

Thus, Simple Interest = $3808

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 = $5950 + $3808

= $9758

Thus, Amount to be paid = $9758 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 = $5950

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5950 + ($5950 × 8% × 8)

= $5950 + ($5950 ×⁸/₁₀₀ × 8)

= $5950 + (^{5950 × 8 × 8}/₁₀₀)

= $5950 + (^{47600 × 8}/₁₀₀)

= $5950 + (³⁸⁰⁸⁰⁰/₁₀₀)

= $5950 + $3808 = $9758

Thus, Amount (A) to be paid = $9758 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 $5950, the simple interest in 1 year

= ⁸/₁₀₀ × 5950

= ^{8 × 5950}/₁₀₀

= ⁴⁷⁶⁰⁰/₁₀₀ = $476

Thus, simple interest for 1 year = $476

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $476 × 8 = $3808

Thus, Simple Interest (SI) = $3808

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5950 + $3808

= $9758

Thus, Amount to be paid = $9758 Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.