Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $8400

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$8400 = P (1 + 4% × 5)

⇒ $8400 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8400 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8400 = P (1 + ²⁰/₁₀₀)

⇒ $8400 = P (^{100 + 20}/₁₀₀)

⇒ $8400 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8400

⇒ P = ⁸⁴⁰⁰/_¹²⁰/100

⇒ P = 8400 × ¹⁰⁰/₁₂₀

⇒ P = ^{8400 × 100}/₁₂₀

⇒ P = ⁸⁴⁰⁰⁰⁰/₁₂₀

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8400, then the Principal = ¹⁰⁰/₁₂₀ × 8400

= ^{100 × 8400}/₁₂₀

= ⁸⁴⁰⁰⁰⁰/₁₂₀

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(2) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.

(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(6) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(9) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(10) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.