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) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(6) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(8) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?