Simple Interest
Math MCQs

Question :    How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?

Correct Answer  $5450

Solution & Explanation

Solution

Given,

Amount (A) = $6812.5

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

$6812.5 = P (1 + 5% × 5)

⇒ $6812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6812.5 = P (1 + ²⁵/₁₀₀)

⇒ $6812.5 = P (^{100 + 25}/₁₀₀)

⇒ $6812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6812.5

⇒ P = ^6812.5/_¹²⁵/100

⇒ P = 6812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6812.5 × 100}/₁₂₅

⇒ P = ⁶⁸¹²⁵⁰/₁₂₅

⇒ P = $5450

Thus, the sum borrowed (P) = $5450 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 6812.5, then the Principal = ¹⁰⁰/₁₂₅ × 6812.5

= ^{100 × 6812.5}/₁₂₅

= ⁶⁸¹²⁵⁰/₁₂₅

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer

Similar Questions

(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?

(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(8) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.