Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $7975

Rate of Simple Interest (R) = 2%

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

$7975 = P (1 + 2% × 5)

⇒ $7975 = P (1 + ²/₁₀₀ × 5)

⇒ $7975 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7975 = P (1 + ¹⁰/₁₀₀)

⇒ $7975 = P (^{100 + 10}/₁₀₀)

⇒ $7975 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7975

⇒ P = ⁷⁹⁷⁵/_¹¹⁰/100

⇒ P = 7975 × ¹⁰⁰/₁₁₀

⇒ P = ^{7975 × 100}/₁₁₀

⇒ P = ⁷⁹⁷⁵⁰⁰/₁₁₀

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7975, then the Principal = ¹⁰⁰/₁₁₀ × 7975

= ^{100 × 7975}/₁₁₀

= ⁷⁹⁷⁵⁰⁰/₁₁₀

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(4) 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.

(5) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

(8) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.