Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $7425

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

$7425 = P (1 + 2% × 5)

⇒ $7425 = P (1 + ²/₁₀₀ × 5)

⇒ $7425 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7425 = P (1 + ¹⁰/₁₀₀)

⇒ $7425 = P (^{100 + 10}/₁₀₀)

⇒ $7425 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7425

⇒ P = ⁷⁴²⁵/_¹¹⁰/100

⇒ P = 7425 × ¹⁰⁰/₁₁₀

⇒ P = ^{7425 × 100}/₁₁₀

⇒ P = ⁷⁴²⁵⁰⁰/₁₁₀

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 7425, then the Principal = ¹⁰⁰/₁₁₀ × 7425

= ^{100 × 7425}/₁₁₀

= ⁷⁴²⁵⁰⁰/₁₁₀

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(8) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.