Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $8797.5

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

$8797.5 = P (1 + 3% × 5)

⇒ $8797.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8797.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8797.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8797.5 = P (^{100 + 15}/₁₀₀)

⇒ $8797.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8797.5

⇒ P = ^8797.5/_¹¹⁵/100

⇒ P = 8797.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8797.5 × 100}/₁₁₅

⇒ P = ⁸⁷⁹⁷⁵⁰/₁₁₅

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 8797.5, then the Principal = ¹⁰⁰/₁₁₅ × 8797.5

= ^{100 × 8797.5}/₁₁₅

= ⁸⁷⁹⁷⁵⁰/₁₁₅

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.

(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

(6) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.