Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $6930

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

$6930 = P (1 + 2% × 5)

⇒ $6930 = P (1 + ²/₁₀₀ × 5)

⇒ $6930 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6930 = P (1 + ¹⁰/₁₀₀)

⇒ $6930 = P (^{100 + 10}/₁₀₀)

⇒ $6930 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6930

⇒ P = ⁶⁹³⁰/_¹¹⁰/100

⇒ P = 6930 × ¹⁰⁰/₁₁₀

⇒ P = ^{6930 × 100}/₁₁₀

⇒ P = ⁶⁹³⁰⁰⁰/₁₁₀

⇒ P = $6300

Thus, the sum borrowed (P) = $6300 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 6930, then the Principal = ¹⁰⁰/₁₁₀ × 6930

= ^{100 × 6930}/₁₁₀

= ⁶⁹³⁰⁰⁰/₁₁₀

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

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

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?