Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

Correct Answer  $8625

Solution & Explanation

Solution

Given,

Principal (P) = $5750

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) = $5750 × 5% × 10

= $5750 ×⁵/₁₀₀ × 10

= ^{5750 × 5 × 10}/₁₀₀

= ^{28750 × 10}/₁₀₀

= ²⁸⁷⁵⁰⁰/₁₀₀

= $2875

Thus, Simple Interest = $2875

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 = $5750 + $2875

= $8625

Thus, Amount to be paid = $8625 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 = $5750

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5750 + ($5750 × 5% × 10)

= $5750 + ($5750 ×⁵/₁₀₀ × 10)

= $5750 + (^{5750 × 5 × 10}/₁₀₀)

= $5750 + (^{28750 × 10}/₁₀₀)

= $5750 + (²⁸⁷⁵⁰⁰/₁₀₀)

= $5750 + $2875 = $8625

Thus, Amount (A) to be paid = $8625 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 $5750, the simple interest in 1 year

= ⁵/₁₀₀ × 5750

= ^{5 × 5750}/₁₀₀

= ²⁸⁷⁵⁰/₁₀₀ = $287.5

Thus, simple interest for 1 year = $287.5

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $287.5 × 10 = $2875

Thus, Simple Interest (SI) = $2875

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $2875

= $8625

Thus, Amount to be paid = $8625 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(2) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?