Simple Interest
Math MCQs

Question :    Kenneth had to pay $5600 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  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5600

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

$5600 = P (1 + 4% × 3)

⇒ $5600 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5600 = P (1 + ^{4 × 3}/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 = 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 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) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(4) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(8) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.