Simple Interest
Math MCQs

Question :    James had to pay $3450 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  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3450

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

$3450 = P (1 + 5% × 3)

⇒ $3450 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3450 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3450 = P (1 + ¹⁵/₁₀₀)

⇒ $3450 = P (^{100 + 15}/₁₀₀)

⇒ $3450 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3450

⇒ P = ³⁴⁵⁰/_¹¹⁵/100

⇒ P = 3450 × ¹⁰⁰/₁₁₅

⇒ P = ^{3450 × 100}/₁₁₅

⇒ P = ³⁴⁵⁰⁰⁰/₁₁₅

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3450, then the Principal = ¹⁰⁰/₁₁₅ × 3450

= ^{100 × 3450}/₁₁₅

= ³⁴⁵⁰⁰⁰/₁₁₅

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(2) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.

(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.

(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?