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) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.

(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(5) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.

(7) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.