Question:
If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4806
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
$4806 = P (1 + 2% × 4)
⇒ $4806 = P (1 + 2/100 × 4)
⇒ $4806 = P (1 + 2 × 4/100)
⇒ $4806 = P (1 + 8/100)
⇒ $4806 = P (100 + 8/100)
⇒ $4806 = P × 108/100
⇒ P × 108/100 = $4806
⇒ P = 4806/108/100
⇒ P = 4806 × 100/108
⇒ P = 4806 × 100/108
⇒ P = 480600/108
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 4806, then the Principal = 100/108 × 4806
= 100 × 4806/108
= 480600/108
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(2) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.