Simple Interest
Math MCQs

Question :    Robert had to pay $3379 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  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3379

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

$3379 = P (1 + 3% × 3)

⇒ $3379 = P (1 + ³/₁₀₀ × 3)

⇒ $3379 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3379 = P (1 + ⁹/₁₀₀)

⇒ $3379 = P (^{100 + 9}/₁₀₀)

⇒ $3379 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3379

⇒ P = ³³⁷⁹/_¹⁰⁹/100

⇒ P = 3379 × ¹⁰⁰/₁₀₉

⇒ P = ^{3379 × 100}/₁₀₉

⇒ P = ³³⁷⁹⁰⁰/₁₀₉

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3379, then the Principal = ¹⁰⁰/₁₀₉ × 3379

= ^{100 × 3379}/₁₀₉

= ³³⁷⁹⁰⁰/₁₀₉

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.