Simple Interest
Math MCQs

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

Correct Answer  $9140.5

Solution & Explanation

Solution

Given,

Principal (P) = $5050

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) = $5050 × 9% × 9

= $5050 ×⁹/₁₀₀ × 9

= ^{5050 × 9 × 9}/₁₀₀

= ^{45450 × 9}/₁₀₀

= ⁴⁰⁹⁰⁵⁰/₁₀₀

= $4090.5

Thus, Simple Interest = $4090.5

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 = $5050 + $4090.5

= $9140.5

Thus, Amount to be paid = $9140.5 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 = $5050

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5050 + ($5050 × 9% × 9)

= $5050 + ($5050 ×⁹/₁₀₀ × 9)

= $5050 + (^{5050 × 9 × 9}/₁₀₀)

= $5050 + (^{45450 × 9}/₁₀₀)

= $5050 + (⁴⁰⁹⁰⁵⁰/₁₀₀)

= $5050 + $4090.5 = $9140.5

Thus, Amount (A) to be paid = $9140.5 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 $5050, the simple interest in 1 year

= ⁹/₁₀₀ × 5050

= ^{9 × 5050}/₁₀₀

= ⁴⁵⁴⁵⁰/₁₀₀ = $454.5

Thus, simple interest for 1 year = $454.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $454.5 × 9 = $4090.5

Thus, Simple Interest (SI) = $4090.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $4090.5

= $9140.5

Thus, Amount to be paid = $9140.5 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(3) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

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

(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

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

(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(9) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?