Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $5807.5

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

$5807.5 = P (1 + 3% × 5)

⇒ $5807.5 = P (1 + ³/₁₀₀ × 5)

⇒ $5807.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5807.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5807.5 = P (^{100 + 15}/₁₀₀)

⇒ $5807.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5807.5

⇒ P = ^5807.5/_¹¹⁵/100

⇒ P = 5807.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5807.5 × 100}/₁₁₅

⇒ P = ⁵⁸⁰⁷⁵⁰/₁₁₅

⇒ P = $5050

Thus, the sum borrowed (P) = $5050 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 5807.5, then the Principal = ¹⁰⁰/₁₁₅ × 5807.5

= ^{100 × 5807.5}/₁₁₅

= ⁵⁸⁰⁷⁵⁰/₁₁₅

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(3) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

(5) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.