Simple Interest
Math MCQs

Question :    If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4104

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

$4104 = P (1 + 2% × 4)

⇒ $4104 = P (1 + ²/₁₀₀ × 4)

⇒ $4104 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4104 = P (1 + ⁸/₁₀₀)

⇒ $4104 = P (^{100 + 8}/₁₀₀)

⇒ $4104 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4104

⇒ P = ⁴¹⁰⁴/_¹⁰⁸/100

⇒ P = 4104 × ¹⁰⁰/₁₀₈

⇒ P = ^{4104 × 100}/₁₀₈

⇒ P = ⁴¹⁰⁴⁰⁰/₁₀₈

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4104, then the Principal = ¹⁰⁰/₁₀₈ × 4104

= ^{100 × 4104}/₁₀₈

= ⁴¹⁰⁴⁰⁰/₁₀₈

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(6) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?