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) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.

(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.