Simple Interest
Math MCQs

Question :    Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $4982

Rate of Simple Interest (R) = 2%

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

$4982 = P (1 + 2% × 3)

⇒ $4982 = P (1 + ²/₁₀₀ × 3)

⇒ $4982 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4982 = P (1 + ⁶/₁₀₀)

⇒ $4982 = P (^{100 + 6}/₁₀₀)

⇒ $4982 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4982

⇒ P = ⁴⁹⁸²/_¹⁰⁶/100

⇒ P = 4982 × ¹⁰⁰/₁₀₆

⇒ P = ^{4982 × 100}/₁₀₆

⇒ P = ⁴⁹⁸²⁰⁰/₁₀₆

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4982, then the Principal = ¹⁰⁰/₁₀₆ × 4982

= ^{100 × 4982}/₁₀₆

= ⁴⁹⁸²⁰⁰/₁₀₆

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(2) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(3) 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.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(6) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?