Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9812.5

Rate of Simple Interest (R) = 5%

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

$9812.5 = P (1 + 5% × 5)

⇒ $9812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9812.5 = P (1 + ²⁵/₁₀₀)

⇒ $9812.5 = P (^{100 + 25}/₁₀₀)

⇒ $9812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9812.5

⇒ P = ^9812.5/_¹²⁵/100

⇒ P = 9812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9812.5 × 100}/₁₂₅

⇒ P = ⁹⁸¹²⁵⁰/₁₂₅

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9812.5, then the Principal = ¹⁰⁰/₁₂₅ × 9812.5

= ^{100 × 9812.5}/₁₂₅

= ⁹⁸¹²⁵⁰/₁₂₅

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(7) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(10) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.