Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

Correct Answer  $6695

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 3%

Time (t) = 10 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5150 × 3% × 10

= $5150 ׳/₁₀₀ × 10

= ^{5150 × 3 × 10}/₁₀₀

= ^{15450 × 10}/₁₀₀

= ¹⁵⁴⁵⁰⁰/₁₀₀

= $1545

Thus, Simple Interest = $1545

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 = $5150 + $1545

= $6695

Thus, Amount to be paid = $6695 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 = $5150

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 3% × 10)

= $5150 + ($5150 ׳/₁₀₀ × 10)

= $5150 + (^{5150 × 3 × 10}/₁₀₀)

= $5150 + (^{15450 × 10}/₁₀₀)

= $5150 + (¹⁵⁴⁵⁰⁰/₁₀₀)

= $5150 + $1545 = $6695

Thus, Amount (A) to be paid = $6695 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5150, the simple interest in 1 year

= ³/₁₀₀ × 5150

= ^{3 × 5150}/₁₀₀

= ¹⁵⁴⁵⁰/₁₀₀ = $154.5

Thus, simple interest for 1 year = $154.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $154.5 × 10 = $1545

Thus, Simple Interest (SI) = $1545

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $1545

= $6695

Thus, Amount to be paid = $6695 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(4) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(5) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(9) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(10) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.