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) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(7) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

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

(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.