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 Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.

(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(8) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?