Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

Correct Answer  $4000.5

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 9%

Time (t) = 3 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) = $3150 × 9% × 3

= $3150 ×⁹/₁₀₀ × 3

= ^{3150 × 9 × 3}/₁₀₀

= ^{28350 × 3}/₁₀₀

= ⁸⁵⁰⁵⁰/₁₀₀

= $850.5

Thus, Simple Interest = $850.5

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 = $3150 + $850.5

= $4000.5

Thus, Amount to be paid = $4000.5 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 = $3150

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

And, Time (t) = 3 years

Thus, Amount (A)

= $3150 + ($3150 × 9% × 3)

= $3150 + ($3150 ×⁹/₁₀₀ × 3)

= $3150 + (^{3150 × 9 × 3}/₁₀₀)

= $3150 + (^{28350 × 3}/₁₀₀)

= $3150 + (⁸⁵⁰⁵⁰/₁₀₀)

= $3150 + $850.5 = $4000.5

Thus, Amount (A) to be paid = $4000.5 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 $3150, the simple interest in 1 year

= ⁹/₁₀₀ × 3150

= ^{9 × 3150}/₁₀₀

= ²⁸³⁵⁰/₁₀₀ = $283.5

Thus, simple interest for 1 year = $283.5

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $283.5 × 3 = $850.5

Thus, Simple Interest (SI) = $850.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $850.5

= $4000.5

Thus, Amount to be paid = $4000.5 Answer

Similar Questions

(1) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(3) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(6) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

(7) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(10) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.