Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4368

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4368 = P (1 + 4% × 3)

⇒ $4368 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4368 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4368 = P (1 + ¹²/₁₀₀)

⇒ $4368 = P (^{100 + 12}/₁₀₀)

⇒ $4368 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4368

⇒ P = ⁴³⁶⁸/_¹¹²/100

⇒ P = 4368 × ¹⁰⁰/₁₁₂

⇒ P = ^{4368 × 100}/₁₁₂

⇒ P = ⁴³⁶⁸⁰⁰/₁₁₂

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4368, then the Principal = ¹⁰⁰/₁₁₂ × 4368

= ^{100 × 4368}/₁₁₂

= ⁴³⁶⁸⁰⁰/₁₁₂

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

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

(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.

(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.