Simple Interest
Math MCQs

Question :    If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3840

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

$3840 = P (1 + 5% × 4)

⇒ $3840 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3840 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3840 = P (1 + ²⁰/₁₀₀)

⇒ $3840 = P (^{100 + 20}/₁₀₀)

⇒ $3840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3840

⇒ P = ³⁸⁴⁰/_¹²⁰/100

⇒ P = 3840 × ¹⁰⁰/₁₂₀

⇒ P = ^{3840 × 100}/₁₂₀

⇒ P = ³⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3840, then the Principal = ¹⁰⁰/₁₂₀ × 3840

= ^{100 × 3840}/₁₂₀

= ³⁸⁴⁰⁰⁰/₁₂₀

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?

(2) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(9) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.