Simple Interest
Math MCQs

Question :    Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3597

Rate of Simple Interest (R) = 3%

Time (T) = 3 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$3597 = P (1 + 3% × 3)

⇒ $3597 = P (1 + ³/₁₀₀ × 3)

⇒ $3597 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3597 = P (1 + ⁹/₁₀₀)

⇒ $3597 = P (^{100 + 9}/₁₀₀)

⇒ $3597 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3597

⇒ P = ³⁵⁹⁷/_¹⁰⁹/100

⇒ P = 3597 × ¹⁰⁰/₁₀₉

⇒ P = ^{3597 × 100}/₁₀₉

⇒ P = ³⁵⁹⁷⁰⁰/₁₀₉

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3597, then the Principal = ¹⁰⁰/₁₀₉ × 3597

= ^{100 × 3597}/₁₀₉

= ³⁵⁹⁷⁰⁰/₁₀₉

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(10) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.