Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $6785

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

$6785 = P (1 + 3% × 5)

⇒ $6785 = P (1 + ³/₁₀₀ × 5)

⇒ $6785 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6785 = P (1 + ¹⁵/₁₀₀)

⇒ $6785 = P (^{100 + 15}/₁₀₀)

⇒ $6785 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6785

⇒ P = ⁶⁷⁸⁵/_¹¹⁵/100

⇒ P = 6785 × ¹⁰⁰/₁₁₅

⇒ P = ^{6785 × 100}/₁₁₅

⇒ P = ⁶⁷⁸⁵⁰⁰/₁₁₅

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 6785, then the Principal = ¹⁰⁰/₁₁₅ × 6785

= ^{100 × 6785}/₁₁₅

= ⁶⁷⁸⁵⁰⁰/₁₁₅

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.

(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(8) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(10) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.