Simple Interest
Math MCQs

Question :    Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

Correct Answer  $5928

Solution & Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (SI) = 2%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5200 × 2% × 7

= $5200 ײ/₁₀₀ × 7

= ^{5200 × 2 × 7}/₁₀₀

= ^{10400 × 7}/₁₀₀

= ⁷²⁸⁰⁰/₁₀₀

= $728

Thus, Simple Interest = $728

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 = $5200 + $728

= $5928

Thus, Amount to be paid = $5928 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 = $5200

Rate of Simple Interest (SI) or (R) = 2%

And, Time (t) = 7 years

Thus, Amount (A)

= $5200 + ($5200 × 2% × 7)

= $5200 + ($5200 ײ/₁₀₀ × 7)

= $5200 + (^{5200 × 2 × 7}/₁₀₀)

= $5200 + (^{10400 × 7}/₁₀₀)

= $5200 + (⁷²⁸⁰⁰/₁₀₀)

= $5200 + $728 = $5928

Thus, Amount (A) to be paid = $5928 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5200, the simple interest in 1 year

= ²/₁₀₀ × 5200

= ^{2 × 5200}/₁₀₀

= ¹⁰⁴⁰⁰/₁₀₀ = $104

Thus, simple interest for 1 year = $104

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $104 × 7 = $728

Thus, Simple Interest (SI) = $728

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5200 + $728

= $5928

Thus, Amount to be paid = $5928 Answer

Similar Questions

(1) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(2) 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?

(3) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?

(9) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.