Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $8305
Rate of Simple Interest (R) = 2%
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
$8305 = P (1 + 2% × 5)
⇒ $8305 = P (1 + 2/100 × 5)
⇒ $8305 = P (1 + 2 × 5/100)
⇒ $8305 = P (1 + 10/100)
⇒ $8305 = P (100 + 10/100)
⇒ $8305 = P × 110/100
⇒ P × 110/100 = $8305
⇒ P = 8305/110/100
⇒ P = 8305 × 100/110
⇒ P = 8305 × 100/110
⇒ P = 830500/110
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8305, then the Principal = 100/110 × 8305
= 100 × 8305/110
= 830500/110
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(4) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.