Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $8085

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

$8085 = P (1 + 2% × 5)

⇒ $8085 = P (1 + ²/₁₀₀ × 5)

⇒ $8085 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8085 = P (1 + ¹⁰/₁₀₀)

⇒ $8085 = P (^{100 + 10}/₁₀₀)

⇒ $8085 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8085

⇒ P = ⁸⁰⁸⁵/_¹¹⁰/100

⇒ P = 8085 × ¹⁰⁰/₁₁₀

⇒ P = ^{8085 × 100}/₁₁₀

⇒ P = ⁸⁰⁸⁵⁰⁰/₁₁₀

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8085, then the Principal = ¹⁰⁰/₁₁₀ × 8085

= ^{100 × 8085}/₁₁₀

= ⁸⁰⁸⁵⁰⁰/₁₁₀

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(5) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(10) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.