Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

Correct Answer  $10498

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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) = $5800 × 9% × 9

= $5800 ×⁹/₁₀₀ × 9

= ^{5800 × 9 × 9}/₁₀₀

= ^{52200 × 9}/₁₀₀

= ⁴⁶⁹⁸⁰⁰/₁₀₀

= $4698

Thus, Simple Interest = $4698

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 = $5800 + $4698

= $10498

Thus, Amount to be paid = $10498 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 = $5800

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 9 years

Thus, Amount (A)

= $5800 + ($5800 × 9% × 9)

= $5800 + ($5800 ×⁹/₁₀₀ × 9)

= $5800 + (^{5800 × 9 × 9}/₁₀₀)

= $5800 + (^{52200 × 9}/₁₀₀)

= $5800 + (⁴⁶⁹⁸⁰⁰/₁₀₀)

= $5800 + $4698 = $10498

Thus, Amount (A) to be paid = $10498 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 $5800, the simple interest in 1 year

= ⁹/₁₀₀ × 5800

= ^{9 × 5800}/₁₀₀

= ⁵²²⁰⁰/₁₀₀ = $522

Thus, simple interest for 1 year = $522

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $522 × 9 = $4698

Thus, Simple Interest (SI) = $4698

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5800 + $4698

= $10498

Thus, Amount to be paid = $10498 Answer

Similar Questions

(1) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.

(3) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(4) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(6) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.