Simple Interest
Math MCQs

Question :    Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

Correct Answer  $10620

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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) = $5900 × 10% × 8

= $5900 ×¹⁰/₁₀₀ × 8

= ^{5900 × 10 × 8}/₁₀₀

= ^{59000 × 8}/₁₀₀

= ⁴⁷²⁰⁰⁰/₁₀₀

= $4720

Thus, Simple Interest = $4720

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 = $5900 + $4720

= $10620

Thus, Amount to be paid = $10620 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 = $5900

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 8 years

Thus, Amount (A)

= $5900 + ($5900 × 10% × 8)

= $5900 + ($5900 ×¹⁰/₁₀₀ × 8)

= $5900 + (^{5900 × 10 × 8}/₁₀₀)

= $5900 + (^{59000 × 8}/₁₀₀)

= $5900 + (⁴⁷²⁰⁰⁰/₁₀₀)

= $5900 + $4720 = $10620

Thus, Amount (A) to be paid = $10620 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 $5900, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5900

= ^{10 × 5900}/₁₀₀

= ⁵⁹⁰⁰⁰/₁₀₀ = $590

Thus, simple interest for 1 year = $590

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $590 × 8 = $4720

Thus, Simple Interest (SI) = $4720

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $4720

= $10620

Thus, Amount to be paid = $10620 Answer

Similar Questions

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

(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.

(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(6) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.