Simple Interest
Math MCQs

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

Correct Answer  $7897

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (SI) = 7%

Time (t) = 7 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) = $5300 × 7% × 7

= $5300 ×⁷/₁₀₀ × 7

= ^{5300 × 7 × 7}/₁₀₀

= ^{37100 × 7}/₁₀₀

= ²⁵⁹⁷⁰⁰/₁₀₀

= $2597

Thus, Simple Interest = $2597

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 + $2597

= $7897

Thus, Amount to be paid = $7897 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) = 7%

And, Time (t) = 7 years

Thus, Amount (A)

= $5300 + ($5300 × 7% × 7)

= $5300 + ($5300 ×⁷/₁₀₀ × 7)

= $5300 + (^{5300 × 7 × 7}/₁₀₀)

= $5300 + (^{37100 × 7}/₁₀₀)

= $5300 + (²⁵⁹⁷⁰⁰/₁₀₀)

= $5300 + $2597 = $7897

Thus, Amount (A) to be paid = $7897 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 $5300, the simple interest in 1 year

= ⁷/₁₀₀ × 5300

= ^{7 × 5300}/₁₀₀

= ³⁷¹⁰⁰/₁₀₀ = $371

Thus, simple interest for 1 year = $371

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $371 × 7 = $2597

Thus, Simple Interest (SI) = $2597

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5300 + $2597

= $7897

Thus, Amount to be paid = $7897 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(4) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(6) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(7) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(9) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.