Simple Interest
Math MCQs

Question :    If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4872

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$4872 = P (1 + 3% × 4)

⇒ $4872 = P (1 + ³/₁₀₀ × 4)

⇒ $4872 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4872 = P (1 + ¹²/₁₀₀)

⇒ $4872 = P (^{100 + 12}/₁₀₀)

⇒ $4872 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4872

⇒ P = ⁴⁸⁷²/_¹¹²/100

⇒ P = 4872 × ¹⁰⁰/₁₁₂

⇒ P = ^{4872 × 100}/₁₁₂

⇒ P = ⁴⁸⁷²⁰⁰/₁₁₂

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 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 4872, then the Principal = ¹⁰⁰/₁₁₂ × 4872

= ^{100 × 4872}/₁₁₂

= ⁴⁸⁷²⁰⁰/₁₁₂

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(4) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.