Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

Correct Answer  $8025

Solution & Explanation

Solution

Given,

Principal (P) = $5350

Rate of Simple Interest (SI) = 5%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5350 × 5% × 10

= $5350 ×⁵/₁₀₀ × 10

= ^{5350 × 5 × 10}/₁₀₀

= ^{26750 × 10}/₁₀₀

= ²⁶⁷⁵⁰⁰/₁₀₀

= $2675

Thus, Simple Interest = $2675

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 = $5350 + $2675

= $8025

Thus, Amount to be paid = $8025 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 = $5350

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 10 years

Thus, Amount (A)

= $5350 + ($5350 × 5% × 10)

= $5350 + ($5350 ×⁵/₁₀₀ × 10)

= $5350 + (^{5350 × 5 × 10}/₁₀₀)

= $5350 + (^{26750 × 10}/₁₀₀)

= $5350 + (²⁶⁷⁵⁰⁰/₁₀₀)

= $5350 + $2675 = $8025

Thus, Amount (A) to be paid = $8025 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5350, the simple interest in 1 year

= ⁵/₁₀₀ × 5350

= ^{5 × 5350}/₁₀₀

= ²⁶⁷⁵⁰/₁₀₀ = $267.5

Thus, simple interest for 1 year = $267.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $267.5 × 10 = $2675

Thus, Simple Interest (SI) = $2675

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5350 + $2675

= $8025

Thus, Amount to be paid = $8025 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(3) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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

(5) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

(6) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(8) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(10) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.