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) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.

(3) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?

(6) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.