Simple Interest
Math MCQs

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

Correct Answer  $10300

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 10%

Time (t) = 10 years

Thus, Amount (A) = ?

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

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

= $5150 ×¹⁰/₁₀₀ × 10

= ^{5150 × 10 × 10}/₁₀₀

= ^{51500 × 10}/₁₀₀

= ⁵¹⁵⁰⁰⁰/₁₀₀

= $5150

Thus, Simple Interest = $5150

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 + $5150

= $10300

Thus, Amount to be paid = $10300 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) = 10%

And, Time (t) = 10 years

Thus, Amount (A)

= $5150 + ($5150 × 10% × 10)

= $5150 + ($5150 ×¹⁰/₁₀₀ × 10)

= $5150 + (^{5150 × 10 × 10}/₁₀₀)

= $5150 + (^{51500 × 10}/₁₀₀)

= $5150 + (⁵¹⁵⁰⁰⁰/₁₀₀)

= $5150 + $5150 = $10300

Thus, Amount (A) to be paid = $10300 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5150, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5150

= ^{10 × 5150}/₁₀₀

= ⁵¹⁵⁰⁰/₁₀₀ = $515

Thus, simple interest for 1 year = $515

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $515 × 10 = $5150

Thus, Simple Interest (SI) = $5150

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $5150

= $10300

Thus, Amount to be paid = $10300 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(4) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(8) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(10) 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.