Question:
If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5238
Rate of Simple Interest (R) = 2%
Time (T) = 4 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
$5238 = P (1 + 2% × 4)
⇒ $5238 = P (1 + 2/100 × 4)
⇒ $5238 = P (1 + 2 × 4/100)
⇒ $5238 = P (1 + 8/100)
⇒ $5238 = P (100 + 8/100)
⇒ $5238 = P × 108/100
⇒ P × 108/100 = $5238
⇒ P = 5238/108/100
⇒ P = 5238 × 100/108
⇒ P = 5238 × 100/108
⇒ P = 523800/108
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5238, then the Principal = 100/108 × 5238
= 100 × 5238/108
= 523800/108
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(4) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(7) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(8) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.