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 Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(8) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(9) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(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.