Simple Interest
Math MCQs

Question :    Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3869.5

Rate of Simple Interest (R) = 3%

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

$3869.5 = P (1 + 3% × 3)

⇒ $3869.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3869.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3869.5 = P (1 + ⁹/₁₀₀)

⇒ $3869.5 = P (^{100 + 9}/₁₀₀)

⇒ $3869.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3869.5

⇒ P = ^3869.5/_¹⁰⁹/100

⇒ P = 3869.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3869.5 × 100}/₁₀₉

⇒ P = ³⁸⁶⁹⁵⁰/₁₀₉

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3869.5, then the Principal = ¹⁰⁰/₁₀₉ × 3869.5

= ^{100 × 3869.5}/₁₀₉

= ³⁸⁶⁹⁵⁰/₁₀₉

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(4) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

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

(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.