Simple Interest
Math MCQs

Question :    Lisa had to pay $4414.5 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  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4414.5

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

$4414.5 = P (1 + 3% × 3)

⇒ $4414.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4414.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4414.5 = P (1 + ⁹/₁₀₀)

⇒ $4414.5 = P (^{100 + 9}/₁₀₀)

⇒ $4414.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4414.5

⇒ P = ^4414.5/_¹⁰⁹/100

⇒ P = 4414.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4414.5 × 100}/₁₀₉

⇒ P = ⁴⁴¹⁴⁵⁰/₁₀₉

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4414.5, then the Principal = ¹⁰⁰/₁₀₉ × 4414.5

= ^{100 × 4414.5}/₁₀₉

= ⁴⁴¹⁴⁵⁰/₁₀₉

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(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) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

(5) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.