Simple Interest
Math MCQs

Question :    Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

Correct Answer  $3904

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (SI) = 7%

Time (t) = 4 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) = $3050 × 7% × 4

= $3050 ×⁷/₁₀₀ × 4

= ^{3050 × 7 × 4}/₁₀₀

= ^{21350 × 4}/₁₀₀

= ⁸⁵⁴⁰⁰/₁₀₀

= $854

Thus, Simple Interest = $854

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 = $3050 + $854

= $3904

Thus, Amount to be paid = $3904 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 = $3050

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

And, Time (t) = 4 years

Thus, Amount (A)

= $3050 + ($3050 × 7% × 4)

= $3050 + ($3050 ×⁷/₁₀₀ × 4)

= $3050 + (^{3050 × 7 × 4}/₁₀₀)

= $3050 + (^{21350 × 4}/₁₀₀)

= $3050 + (⁸⁵⁴⁰⁰/₁₀₀)

= $3050 + $854 = $3904

Thus, Amount (A) to be paid = $3904 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 $3050, the simple interest in 1 year

= ⁷/₁₀₀ × 3050

= ^{7 × 3050}/₁₀₀

= ²¹³⁵⁰/₁₀₀ = $213.5

Thus, simple interest for 1 year = $213.5

Therefore, simple interest for 4 years

= Simple interest for 1 year × 4

= $213.5 × 4 = $854

Thus, Simple Interest (SI) = $854

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3050 + $854

= $3904

Thus, Amount to be paid = $3904 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(4) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.