Simple Interest
Math MCQs

Question :    If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3672

Rate of Simple Interest (R) = 2%

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

$3672 = P (1 + 2% × 4)

⇒ $3672 = P (1 + ²/₁₀₀ × 4)

⇒ $3672 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3672 = P (1 + ⁸/₁₀₀)

⇒ $3672 = P (^{100 + 8}/₁₀₀)

⇒ $3672 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3672

⇒ P = ³⁶⁷²/_¹⁰⁸/100

⇒ P = 3672 × ¹⁰⁰/₁₀₈

⇒ P = ^{3672 × 100}/₁₀₈

⇒ P = ³⁶⁷²⁰⁰/₁₀₈

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3672, then the Principal = ¹⁰⁰/₁₀₈ × 3672

= ^{100 × 3672}/₁₀₈

= ³⁶⁷²⁰⁰/₁₀₈

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(3) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

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

(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.