Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Margaret had to pay $5002.5 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $5002.5

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

$5002.5 = P (1 + 5% × 3)

⇒ $5002.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5002.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5002.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5002.5 = P (^{100 + 15}/₁₀₀)

⇒ $5002.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5002.5

⇒ P = ^5002.5/_¹¹⁵/100

⇒ P = 5002.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5002.5 × 100}/₁₁₅

⇒ P = ⁵⁰⁰²⁵⁰/₁₁₅

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 5002.5, then the Principal = ¹⁰⁰/₁₁₅ × 5002.5

= ^{100 × 5002.5}/₁₁₅

= ⁵⁰⁰²⁵⁰/₁₁₅

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(6) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(10) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.