Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $6490

Rate of Simple Interest (R) = 2%

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

$6490 = P (1 + 2% × 5)

⇒ $6490 = P (1 + ²/₁₀₀ × 5)

⇒ $6490 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6490 = P (1 + ¹⁰/₁₀₀)

⇒ $6490 = P (^{100 + 10}/₁₀₀)

⇒ $6490 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6490

⇒ P = ⁶⁴⁹⁰/_¹¹⁰/100

⇒ P = 6490 × ¹⁰⁰/₁₁₀

⇒ P = ^{6490 × 100}/₁₁₀

⇒ P = ⁶⁴⁹⁰⁰⁰/₁₁₀

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6490, then the Principal = ¹⁰⁰/₁₁₀ × 6490

= ^{100 × 6490}/₁₁₀

= ⁶⁴⁹⁰⁰⁰/₁₁₀

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

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

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(6) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(8) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.