Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $6900

Rate of Simple Interest (R) = 3%

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

$6900 = P (1 + 3% × 5)

⇒ $6900 = P (1 + ³/₁₀₀ × 5)

⇒ $6900 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6900 = P (1 + ¹⁵/₁₀₀)

⇒ $6900 = P (^{100 + 15}/₁₀₀)

⇒ $6900 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6900

⇒ P = ⁶⁹⁰⁰/_¹¹⁵/100

⇒ P = 6900 × ¹⁰⁰/₁₁₅

⇒ P = ^{6900 × 100}/₁₁₅

⇒ P = ⁶⁹⁰⁰⁰⁰/₁₁₅

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6900, then the Principal = ¹⁰⁰/₁₁₅ × 6900

= ^{100 × 6900}/₁₁₅

= ⁶⁹⁰⁰⁰⁰/₁₁₅

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(3) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

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

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.

(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.

(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.