Simple Interest
Math MCQs

Question :    Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

Correct Answer  $7155

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (SI) = 5%

Time (t) = 7 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) = $5300 × 5% × 7

= $5300 ×⁵/₁₀₀ × 7

= ^{5300 × 5 × 7}/₁₀₀

= ^{26500 × 7}/₁₀₀

= ¹⁸⁵⁵⁰⁰/₁₀₀

= $1855

Thus, Simple Interest = $1855

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 = $5300 + $1855

= $7155

Thus, Amount to be paid = $7155 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 = $5300

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5300 + ($5300 × 5% × 7)

= $5300 + ($5300 ×⁵/₁₀₀ × 7)

= $5300 + (^{5300 × 5 × 7}/₁₀₀)

= $5300 + (^{26500 × 7}/₁₀₀)

= $5300 + (¹⁸⁵⁵⁰⁰/₁₀₀)

= $5300 + $1855 = $7155

Thus, Amount (A) to be paid = $7155 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 $5300, the simple interest in 1 year

= ⁵/₁₀₀ × 5300

= ^{5 × 5300}/₁₀₀

= ²⁶⁵⁰⁰/₁₀₀ = $265

Thus, simple interest for 1 year = $265

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $265 × 7 = $1855

Thus, Simple Interest (SI) = $1855

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5300 + $1855

= $7155

Thus, Amount to be paid = $7155 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(2) If Karen borrowed $3950 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 if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(4) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(8) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.