Simple Interest
Math MCQs

Question :    If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3618

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

$3618 = P (1 + 2% × 4)

⇒ $3618 = P (1 + ²/₁₀₀ × 4)

⇒ $3618 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3618 = P (1 + ⁸/₁₀₀)

⇒ $3618 = P (^{100 + 8}/₁₀₀)

⇒ $3618 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3618

⇒ P = ³⁶¹⁸/_¹⁰⁸/100

⇒ P = 3618 × ¹⁰⁰/₁₀₈

⇒ P = ^{3618 × 100}/₁₀₈

⇒ P = ³⁶¹⁸⁰⁰/₁₀₈

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3618, then the Principal = ¹⁰⁰/₁₀₈ × 3618

= ^{100 × 3618}/₁₀₈

= ³⁶¹⁸⁰⁰/₁₀₈

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.

(5) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.