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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(6) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.