Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

Correct Answer  $10588.5

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 9%

Time (t) = 9 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) = $5850 × 9% × 9

= $5850 ×⁹/₁₀₀ × 9

= ^{5850 × 9 × 9}/₁₀₀

= ^{52650 × 9}/₁₀₀

= ⁴⁷³⁸⁵⁰/₁₀₀

= $4738.5

Thus, Simple Interest = $4738.5

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 + $4738.5

= $10588.5

Thus, Amount to be paid = $10588.5 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) = 9%

And, Time (t) = 9 years

Thus, Amount (A)

= $5850 + ($5850 × 9% × 9)

= $5850 + ($5850 ×⁹/₁₀₀ × 9)

= $5850 + (^{5850 × 9 × 9}/₁₀₀)

= $5850 + (^{52650 × 9}/₁₀₀)

= $5850 + (⁴⁷³⁸⁵⁰/₁₀₀)

= $5850 + $4738.5 = $10588.5

Thus, Amount (A) to be paid = $10588.5 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 $5850, the simple interest in 1 year

= ⁹/₁₀₀ × 5850

= ^{9 × 5850}/₁₀₀

= ⁵²⁶⁵⁰/₁₀₀ = $526.5

Thus, simple interest for 1 year = $526.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $526.5 × 9 = $4738.5

Thus, Simple Interest (SI) = $4738.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $4738.5

= $10588.5

Thus, Amount to be paid = $10588.5 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(2) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(4) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(7) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.