Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6875

Rate of Simple Interest (R) = 5%

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

$6875 = P (1 + 5% × 5)

⇒ $6875 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6875 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6875 = P (1 + ²⁵/₁₀₀)

⇒ $6875 = P (^{100 + 25}/₁₀₀)

⇒ $6875 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6875

⇒ P = ⁶⁸⁷⁵/_¹²⁵/100

⇒ P = 6875 × ¹⁰⁰/₁₂₅

⇒ P = ^{6875 × 100}/₁₂₅

⇒ P = ⁶⁸⁷⁵⁰⁰/₁₂₅

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6875, then the Principal = ¹⁰⁰/₁₂₅ × 6875

= ^{100 × 6875}/₁₂₅

= ⁶⁸⁷⁵⁰⁰/₁₂₅

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

(3) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.

(5) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(8) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?