Simple Interest
Math MCQs

Question :    Richard had to pay $4140 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4140

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

$4140 = P (1 + 5% × 3)

⇒ $4140 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4140 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4140 = P (1 + ¹⁵/₁₀₀)

⇒ $4140 = P (^{100 + 15}/₁₀₀)

⇒ $4140 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4140

⇒ P = ⁴¹⁴⁰/_¹¹⁵/100

⇒ P = 4140 × ¹⁰⁰/₁₁₅

⇒ P = ^{4140 × 100}/₁₁₅

⇒ P = ⁴¹⁴⁰⁰⁰/₁₁₅

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 4140, then the Principal = ¹⁰⁰/₁₁₅ × 4140

= ^{100 × 4140}/₁₁₅

= ⁴¹⁴⁰⁰⁰/₁₁₅

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.