Simple Interest
Math MCQs

Question :    If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4592

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

$4592 = P (1 + 3% × 4)

⇒ $4592 = P (1 + ³/₁₀₀ × 4)

⇒ $4592 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4592 = P (1 + ¹²/₁₀₀)

⇒ $4592 = P (^{100 + 12}/₁₀₀)

⇒ $4592 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4592

⇒ P = ⁴⁵⁹²/_¹¹²/100

⇒ P = 4592 × ¹⁰⁰/₁₁₂

⇒ P = ^{4592 × 100}/₁₁₂

⇒ P = ⁴⁵⁹²⁰⁰/₁₁₂

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4592, then the Principal = ¹⁰⁰/₁₁₂ × 4592

= ^{100 × 4592}/₁₁₂

= ⁴⁵⁹²⁰⁰/₁₁₂

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(3) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(7) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?

(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

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