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) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

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

(5) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(8) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.