Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $8562.5
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
$8562.5 = P (1 + 5% × 5)
⇒ $8562.5 = P (1 + 5/100 × 5)
⇒ $8562.5 = P (1 + 5 × 5/100)
⇒ $8562.5 = P (1 + 25/100)
⇒ $8562.5 = P (100 + 25/100)
⇒ $8562.5 = P × 125/100
⇒ P × 125/100 = $8562.5
⇒ P = 8562.5/125/100
⇒ P = 8562.5 × 100/125
⇒ P = 8562.5 × 100/125
⇒ P = 856250/125
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 8562.5, then the Principal = 100/125 × 8562.5
= 100 × 8562.5/125
= 856250/125
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(6) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(10) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.