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) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(3) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(5) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.

(8) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

(9) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.