Simple Interest
Math MCQs

Question :    How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

Correct Answer  $5200

Solution & Explanation

Solution

Given,

Amount (A) = $5720

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

$5720 = P (1 + 2% × 5)

⇒ $5720 = P (1 + ²/₁₀₀ × 5)

⇒ $5720 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5720 = P (1 + ¹⁰/₁₀₀)

⇒ $5720 = P (^{100 + 10}/₁₀₀)

⇒ $5720 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5720

⇒ P = ⁵⁷²⁰/_¹¹⁰/100

⇒ P = 5720 × ¹⁰⁰/₁₁₀

⇒ P = ^{5720 × 100}/₁₁₀

⇒ P = ⁵⁷²⁰⁰⁰/₁₁₀

⇒ P = $5200

Thus, the sum borrowed (P) = $5200 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 5720, then the Principal = ¹⁰⁰/₁₁₀ × 5720

= ^{100 × 5720}/₁₁₀

= ⁵⁷²⁰⁰⁰/₁₁₀

= 5200

Thus, Principal = $5200

Thus, the sum borrowed = $5200 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

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

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

(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(8) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?