Simple Interest
Math MCQs

Question :    How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

Correct Answer  $6400

Solution & Explanation

Solution

Given,

Amount (A) = $7040

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

$7040 = P (1 + 2% × 5)

⇒ $7040 = P (1 + ²/₁₀₀ × 5)

⇒ $7040 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7040 = P (1 + ¹⁰/₁₀₀)

⇒ $7040 = P (^{100 + 10}/₁₀₀)

⇒ $7040 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7040

⇒ P = ⁷⁰⁴⁰/_¹¹⁰/100

⇒ P = 7040 × ¹⁰⁰/₁₁₀

⇒ P = ^{7040 × 100}/₁₁₀

⇒ P = ⁷⁰⁴⁰⁰⁰/₁₁₀

⇒ P = $6400

Thus, the sum borrowed (P) = $6400 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 7040, then the Principal = ¹⁰⁰/₁₁₀ × 7040

= ^{100 × 7040}/₁₁₀

= ⁷⁰⁴⁰⁰⁰/₁₁₀

= 6400

Thus, Principal = $6400

Thus, the sum borrowed = $6400 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.

(3) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?