Simple Interest
Math MCQs

Question :    How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

Correct Answer  $7200

Solution & Explanation

Solution

Given,

Amount (A) = $7920

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

$7920 = P (1 + 2% × 5)

⇒ $7920 = P (1 + ²/₁₀₀ × 5)

⇒ $7920 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7920 = P (1 + ¹⁰/₁₀₀)

⇒ $7920 = P (^{100 + 10}/₁₀₀)

⇒ $7920 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7920

⇒ P = ⁷⁹²⁰/_¹¹⁰/100

⇒ P = 7920 × ¹⁰⁰/₁₁₀

⇒ P = ^{7920 × 100}/₁₁₀

⇒ P = ⁷⁹²⁰⁰⁰/₁₁₀

⇒ P = $7200

Thus, the sum borrowed (P) = $7200 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 7920, then the Principal = ¹⁰⁰/₁₁₀ × 7920

= ^{100 × 7920}/₁₁₀

= ⁷⁹²⁰⁰⁰/₁₁₀

= 7200

Thus, Principal = $7200

Thus, the sum borrowed = $7200 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(8) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.