Simple Interest
Math MCQs

Question :    James had to pay $3270 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  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3270

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

$3270 = P (1 + 3% × 3)

⇒ $3270 = P (1 + ³/₁₀₀ × 3)

⇒ $3270 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3270 = P (1 + ⁹/₁₀₀)

⇒ $3270 = P (^{100 + 9}/₁₀₀)

⇒ $3270 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3270

⇒ P = ³²⁷⁰/_¹⁰⁹/100

⇒ P = 3270 × ¹⁰⁰/₁₀₉

⇒ P = ^{3270 × 100}/₁₀₉

⇒ P = ³²⁷⁰⁰⁰/₁₀₉

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3270, then the Principal = ¹⁰⁰/₁₀₉ × 3270

= ^{100 × 3270}/₁₀₉

= ³²⁷⁰⁰⁰/₁₀₉

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

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

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.