Simple Interest
Math MCQs

Question :    If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5600

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

$5600 = P (1 + 3% × 4)

⇒ $5600 = P (1 + ³/₁₀₀ × 4)

⇒ $5600 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5600 = P (1 + ¹²/₁₀₀)

⇒ $5600 = P (^{100 + 12}/₁₀₀)

⇒ $5600 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5600

⇒ P = ⁵⁶⁰⁰/_¹¹²/100

⇒ P = 5600 × ¹⁰⁰/₁₁₂

⇒ P = ^{5600 × 100}/₁₁₂

⇒ P = ⁵⁶⁰⁰⁰⁰/₁₁₂

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5600, then the Principal = ¹⁰⁰/₁₁₂ × 5600

= ^{100 × 5600}/₁₁₂

= ⁵⁶⁰⁰⁰⁰/₁₁₂

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.

(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(10) 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.