Simple Interest
Math MCQs

Question :    Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3795

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$3795 = P (1 + 5% × 3)

⇒ $3795 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3795 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3795 = P (1 + ¹⁵/₁₀₀)

⇒ $3795 = P (^{100 + 15}/₁₀₀)

⇒ $3795 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3795

⇒ P = ³⁷⁹⁵/_¹¹⁵/100

⇒ P = 3795 × ¹⁰⁰/₁₁₅

⇒ P = ^{3795 × 100}/₁₁₅

⇒ P = ³⁷⁹⁵⁰⁰/₁₁₅

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 3795, then the Principal = ¹⁰⁰/₁₁₅ × 3795

= ^{100 × 3795}/₁₁₅

= ³⁷⁹⁵⁰⁰/₁₁₅

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?

(3) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(8) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?

(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.