Simple Interest
Math MCQs

Question :    Paul had to pay $5123 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  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5123

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

$5123 = P (1 + 3% × 3)

⇒ $5123 = P (1 + ³/₁₀₀ × 3)

⇒ $5123 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5123 = P (1 + ⁹/₁₀₀)

⇒ $5123 = P (^{100 + 9}/₁₀₀)

⇒ $5123 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5123

⇒ P = ⁵¹²³/_¹⁰⁹/100

⇒ P = 5123 × ¹⁰⁰/₁₀₉

⇒ P = ^{5123 × 100}/₁₀₉

⇒ P = ⁵¹²³⁰⁰/₁₀₉

⇒ 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 = 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 5123, then the Principal = ¹⁰⁰/₁₀₉ × 5123

= ^{100 × 5123}/₁₀₉

= ⁵¹²³⁰⁰/₁₀₉

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.