Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

Correct Answer  $11210

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 9%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10

= $5900 ×⁹/₁₀₀ × 10

= ^{5900 × 9 × 10}/₁₀₀

= ^{53100 × 10}/₁₀₀

= ⁵³¹⁰⁰⁰/₁₀₀

= $5310

Thus, Simple Interest = $5310

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 + $5310

= $11210

Thus, Amount to be paid = $11210 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) = 9%

And, Time (t) = 10 years

Thus, Amount (A)

= $5900 + ($5900 × 9% × 10)

= $5900 + ($5900 ×⁹/₁₀₀ × 10)

= $5900 + (^{5900 × 9 × 10}/₁₀₀)

= $5900 + (^{53100 × 10}/₁₀₀)

= $5900 + (⁵³¹⁰⁰⁰/₁₀₀)

= $5900 + $5310 = $11210

Thus, Amount (A) to be paid = $11210 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5900, the simple interest in 1 year

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = $531

Thus, simple interest for 1 year = $531

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $531 × 10 = $5310

Thus, Simple Interest (SI) = $5310

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $5310

= $11210

Thus, Amount to be paid = $11210 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 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) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.