Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $8100

Rate of Simple Interest (R) = 4%

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

$8100 = P (1 + 4% × 5)

⇒ $8100 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8100 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8100 = P (1 + ²⁰/₁₀₀)

⇒ $8100 = P (^{100 + 20}/₁₀₀)

⇒ $8100 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8100

⇒ P = ⁸¹⁰⁰/_¹²⁰/100

⇒ P = 8100 × ¹⁰⁰/₁₂₀

⇒ P = ^{8100 × 100}/₁₂₀

⇒ P = ⁸¹⁰⁰⁰⁰/₁₂₀

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8100, then the Principal = ¹⁰⁰/₁₂₀ × 8100

= ^{100 × 8100}/₁₂₀

= ⁸¹⁰⁰⁰⁰/₁₂₀

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(5) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?