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) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.