Simple Interest
Math MCQs

Question :    If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $6000

Rate of Simple Interest (R) = 5%

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

$6000 = P (1 + 5% × 4)

⇒ $6000 = P (1 + ⁵/₁₀₀ × 4)

⇒ $6000 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $6000 = P (1 + ²⁰/₁₀₀)

⇒ $6000 = P (^{100 + 20}/₁₀₀)

⇒ $6000 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6000

⇒ P = ⁶⁰⁰⁰/_¹²⁰/100

⇒ P = 6000 × ¹⁰⁰/₁₂₀

⇒ P = ^{6000 × 100}/₁₂₀

⇒ P = ⁶⁰⁰⁰⁰⁰/₁₂₀

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 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 6000, then the Principal = ¹⁰⁰/₁₂₀ × 6000

= ^{100 × 6000}/₁₂₀

= ⁶⁰⁰⁰⁰⁰/₁₂₀

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(2) 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.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?