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 Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(9) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.