Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9540

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$9540 = P (1 + 4% × 5)

⇒ $9540 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9540 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9540 = P (1 + ²⁰/₁₀₀)

⇒ $9540 = P (^{100 + 20}/₁₀₀)

⇒ $9540 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9540

⇒ P = ⁹⁵⁴⁰/_¹²⁰/100

⇒ P = 9540 × ¹⁰⁰/₁₂₀

⇒ P = ^{9540 × 100}/₁₂₀

⇒ P = ⁹⁵⁴⁰⁰⁰/₁₂₀

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9540, then the Principal = ¹⁰⁰/₁₂₀ × 9540

= ^{100 × 9540}/₁₂₀

= ⁹⁵⁴⁰⁰⁰/₁₂₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(2) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(5) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(8) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.