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) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(2) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(6) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

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

(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(10) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.