Simple Interest
Math MCQs

Question :    If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3480

Rate of Simple Interest (R) = 4%

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

$3480 = P (1 + 4% × 4)

⇒ $3480 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3480 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3480 = P (1 + ¹⁶/₁₀₀)

⇒ $3480 = P (^{100 + 16}/₁₀₀)

⇒ $3480 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3480

⇒ P = ³⁴⁸⁰/_¹¹⁶/100

⇒ P = 3480 × ¹⁰⁰/₁₁₆

⇒ P = ^{3480 × 100}/₁₁₆

⇒ P = ³⁴⁸⁰⁰⁰/₁₁₆

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3480, then the Principal = ¹⁰⁰/₁₁₆ × 3480

= ^{100 × 3480}/₁₁₆

= ³⁴⁸⁰⁰⁰/₁₁₆

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(2) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(10) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.