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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.

(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(5) 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?

(6) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(10) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.