Simple Interest
Math MCQs

Question :    If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3402

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

$3402 = P (1 + 2% × 4)

⇒ $3402 = P (1 + ²/₁₀₀ × 4)

⇒ $3402 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3402 = P (1 + ⁸/₁₀₀)

⇒ $3402 = P (^{100 + 8}/₁₀₀)

⇒ $3402 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3402

⇒ P = ³⁴⁰²/_¹⁰⁸/100

⇒ P = 3402 × ¹⁰⁰/₁₀₈

⇒ P = ^{3402 × 100}/₁₀₈

⇒ P = ³⁴⁰²⁰⁰/₁₀₈

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3402, then the Principal = ¹⁰⁰/₁₀₈ × 3402

= ^{100 × 3402}/₁₀₈

= ³⁴⁰²⁰⁰/₁₀₈

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

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

(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.

(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.