Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $5610

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

$5610 = P (1 + 2% × 5)

⇒ $5610 = P (1 + ²/₁₀₀ × 5)

⇒ $5610 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5610 = P (1 + ¹⁰/₁₀₀)

⇒ $5610 = P (^{100 + 10}/₁₀₀)

⇒ $5610 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5610

⇒ P = ⁵⁶¹⁰/_¹¹⁰/100

⇒ P = 5610 × ¹⁰⁰/₁₁₀

⇒ P = ^{5610 × 100}/₁₁₀

⇒ P = ⁵⁶¹⁰⁰⁰/₁₁₀

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = ¹⁰⁰/₁₁₀ × 5610

= ^{100 × 5610}/₁₁₀

= ⁵⁶¹⁰⁰⁰/₁₁₀

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.

(3) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.

(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(7) 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.

(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.