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) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(3) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.

(10) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?