Simple Interest
Math MCQs

Question :    Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

Correct Answer  $7878

Solution & Explanation

Solution

Given,

Principal (P) = $5050

Rate of Simple Interest (SI) = 7%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5050 × 7% × 8

= $5050 ×⁷/₁₀₀ × 8

= ^{5050 × 7 × 8}/₁₀₀

= ^{35350 × 8}/₁₀₀

= ²⁸²⁸⁰⁰/₁₀₀

= $2828

Thus, Simple Interest = $2828

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 = $5050 + $2828

= $7878

Thus, Amount to be paid = $7878 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 = $5050

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 8 years

Thus, Amount (A)

= $5050 + ($5050 × 7% × 8)

= $5050 + ($5050 ×⁷/₁₀₀ × 8)

= $5050 + (^{5050 × 7 × 8}/₁₀₀)

= $5050 + (^{35350 × 8}/₁₀₀)

= $5050 + (²⁸²⁸⁰⁰/₁₀₀)

= $5050 + $2828 = $7878

Thus, Amount (A) to be paid = $7878 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5050, the simple interest in 1 year

= ⁷/₁₀₀ × 5050

= ^{7 × 5050}/₁₀₀

= ³⁵³⁵⁰/₁₀₀ = $353.5

Thus, simple interest for 1 year = $353.5

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $353.5 × 8 = $2828

Thus, Simple Interest (SI) = $2828

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $2828

= $7878

Thus, Amount to be paid = $7878 Answer

Similar Questions

(1) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(6) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(7) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.