Simple Interest
Math MCQs

Question :    Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

Correct Answer  $7078.5

Solution & Explanation

Solution

Given,

Principal (P) = $5850

Rate of Simple Interest (SI) = 3%

Time (t) = 7 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) = $5850 × 3% × 7

= $5850 ׳/₁₀₀ × 7

= ^{5850 × 3 × 7}/₁₀₀

= ^{17550 × 7}/₁₀₀

= ¹²²⁸⁵⁰/₁₀₀

= $1228.5

Thus, Simple Interest = $1228.5

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 = $5850 + $1228.5

= $7078.5

Thus, Amount to be paid = $7078.5 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 = $5850

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5850 + ($5850 × 3% × 7)

= $5850 + ($5850 ׳/₁₀₀ × 7)

= $5850 + (^{5850 × 3 × 7}/₁₀₀)

= $5850 + (^{17550 × 7}/₁₀₀)

= $5850 + (¹²²⁸⁵⁰/₁₀₀)

= $5850 + $1228.5 = $7078.5

Thus, Amount (A) to be paid = $7078.5 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 $5850, the simple interest in 1 year

= ³/₁₀₀ × 5850

= ^{3 × 5850}/₁₀₀

= ¹⁷⁵⁵⁰/₁₀₀ = $175.5

Thus, simple interest for 1 year = $175.5

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $175.5 × 7 = $1228.5

Thus, Simple Interest (SI) = $1228.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $1228.5

= $7078.5

Thus, Amount to be paid = $7078.5 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(5) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(8) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.