Simple Interest
Math MCQs

Question :    Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5040

Rate of Simple Interest (R) = 4%

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

$5040 = P (1 + 4% × 3)

⇒ $5040 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5040 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5040 = P (1 + ¹²/₁₀₀)

⇒ $5040 = P (^{100 + 12}/₁₀₀)

⇒ $5040 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5040

⇒ P = ⁵⁰⁴⁰/_¹¹²/100

⇒ P = 5040 × ¹⁰⁰/₁₁₂

⇒ P = ^{5040 × 100}/₁₁₂

⇒ P = ⁵⁰⁴⁰⁰⁰/₁₁₂

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5040, then the Principal = ¹⁰⁰/₁₁₂ × 5040

= ^{100 × 5040}/₁₁₂

= ⁵⁰⁴⁰⁰⁰/₁₁₂

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.

(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(5) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

(7) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.