Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

Correct Answer  $4284

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 9%

Time (t) = 4 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% × 4

= $3150 ×⁹/₁₀₀ × 4

= ^{3150 × 9 × 4}/₁₀₀

= ^{28350 × 4}/₁₀₀

= ¹¹³⁴⁰⁰/₁₀₀

= $1134

Thus, Simple Interest = $1134

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 + $1134

= $4284

Thus, Amount to be paid = $4284 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) = 4 years

Thus, Amount (A)

= $3150 + ($3150 × 9% × 4)

= $3150 + ($3150 ×⁹/₁₀₀ × 4)

= $3150 + (^{3150 × 9 × 4}/₁₀₀)

= $3150 + (^{28350 × 4}/₁₀₀)

= $3150 + (¹¹³⁴⁰⁰/₁₀₀)

= $3150 + $1134 = $4284

Thus, Amount (A) to be paid = $4284 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 4 years

= Simple interest for 1 year × 4

= $283.5 × 4 = $1134

Thus, Simple Interest (SI) = $1134

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $1134

= $4284

Thus, Amount to be paid = $4284 Answer

Similar Questions

(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(2) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.

(8) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(9) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?