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) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(3) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.