Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $6600

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

$6600 = P (1 + 2% × 5)

⇒ $6600 = P (1 + ²/₁₀₀ × 5)

⇒ $6600 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6600 = P (1 + ¹⁰/₁₀₀)

⇒ $6600 = P (^{100 + 10}/₁₀₀)

⇒ $6600 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6600

⇒ P = ⁶⁶⁰⁰/_¹¹⁰/100

⇒ P = 6600 × ¹⁰⁰/₁₁₀

⇒ P = ^{6600 × 100}/₁₁₀

⇒ P = ⁶⁶⁰⁰⁰⁰/₁₁₀

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 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 6600, then the Principal = ¹⁰⁰/₁₁₀ × 6600

= ^{100 × 6600}/₁₁₀

= ⁶⁶⁰⁰⁰⁰/₁₁₀

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(4) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(5) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.

(10) 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?