Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6687.5

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

$6687.5 = P (1 + 5% × 5)

⇒ $6687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6687.5 = P (1 + ²⁵/₁₀₀)

⇒ $6687.5 = P (^{100 + 25}/₁₀₀)

⇒ $6687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6687.5

⇒ P = ^6687.5/_¹²⁵/100

⇒ P = 6687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6687.5 × 100}/₁₂₅

⇒ P = ⁶⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 6687.5, then the Principal = ¹⁰⁰/₁₂₅ × 6687.5

= ^{100 × 6687.5}/₁₂₅

= ⁶⁶⁸⁷⁵⁰/₁₂₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(2) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.

(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

(9) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.