Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $8745
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
$8745 = P (1 + 2% × 5)
⇒ $8745 = P (1 + 2/100 × 5)
⇒ $8745 = P (1 + 2 × 5/100)
⇒ $8745 = P (1 + 10/100)
⇒ $8745 = P (100 + 10/100)
⇒ $8745 = P × 110/100
⇒ P × 110/100 = $8745
⇒ P = 8745/110/100
⇒ P = 8745 × 100/110
⇒ P = 8745 × 100/110
⇒ P = 874500/110
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 8745, then the Principal = 100/110 × 8745
= 100 × 8745/110
= 874500/110
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(7) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(10) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.