Simple Interest
Math MCQs

Question :    If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $3996

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

$3996 = P (1 + 2% × 4)

⇒ $3996 = P (1 + ²/₁₀₀ × 4)

⇒ $3996 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3996 = P (1 + ⁸/₁₀₀)

⇒ $3996 = P (^{100 + 8}/₁₀₀)

⇒ $3996 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3996

⇒ P = ³⁹⁹⁶/_¹⁰⁸/100

⇒ P = 3996 × ¹⁰⁰/₁₀₈

⇒ P = ^{3996 × 100}/₁₀₈

⇒ P = ³⁹⁹⁶⁰⁰/₁₀₈

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 3996, then the Principal = ¹⁰⁰/₁₀₈ × 3996

= ^{100 × 3996}/₁₀₈

= ³⁹⁹⁶⁰⁰/₁₀₈

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(2) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(3) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.

(4) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(7) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(9) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.