Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5750

Rate of Simple Interest (R) = 3%

Time (T) = 5 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 + 3% × 5)

⇒ $5750 = P (1 + ³/₁₀₀ × 5)

⇒ $5750 = P (1 + ^{3 × 5}/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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 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) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(4) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.

(6) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.