Simple Interest
Math MCQs

Question :    How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $8395

Rate of Simple Interest (R) = 3%

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

$8395 = P (1 + 3% × 5)

⇒ $8395 = P (1 + ³/₁₀₀ × 5)

⇒ $8395 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8395 = P (1 + ¹⁵/₁₀₀)

⇒ $8395 = P (^{100 + 15}/₁₀₀)

⇒ $8395 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8395

⇒ P = ⁸³⁹⁵/_¹¹⁵/100

⇒ P = 8395 × ¹⁰⁰/₁₁₅

⇒ P = ^{8395 × 100}/₁₁₅

⇒ P = ⁸³⁹⁵⁰⁰/₁₁₅

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 = 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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8395, then the Principal = ¹⁰⁰/₁₁₅ × 8395

= ^{100 × 8395}/₁₁₅

= ⁸³⁹⁵⁰⁰/₁₁₅

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer

Similar Questions

(1) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.