Simple Interest
Math MCQs

Question :    Kenneth had to pay $5750 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  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5750

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

$5750 = P (1 + 5% × 3)

⇒ $5750 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5750 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5750 = P (1 + ¹⁵/₁₀₀)

⇒ $5750 = P (^{100 + 15}/₁₀₀)

⇒ $5750 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5750

⇒ P = ⁵⁷⁵⁰/_¹¹⁵/100

⇒ P = 5750 × ¹⁰⁰/₁₁₅

⇒ P = ^{5750 × 100}/₁₁₅

⇒ P = ⁵⁷⁵⁰⁰⁰/₁₁₅

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5750, then the Principal = ¹⁰⁰/₁₁₅ × 5750

= ^{100 × 5750}/₁₁₅

= ⁵⁷⁵⁰⁰⁰/₁₁₅

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

(3) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.