Question:
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.
Correct Answer
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4984
Rate of Simple Interest (R) = 3%
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
$4984 = P (1 + 3% × 4)
⇒ $4984 = P (1 + 3/100 × 4)
⇒ $4984 = P (1 + 3 × 4/100)
⇒ $4984 = P (1 + 12/100)
⇒ $4984 = P (100 + 12/100)
⇒ $4984 = P × 112/100
⇒ P × 112/100 = $4984
⇒ P = 4984/112/100
⇒ P = 4984 × 100/112
⇒ P = 4984 × 100/112
⇒ P = 498400/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4984, then the Principal = 100/112 × 4984
= 100 × 4984/112
= 498400/112
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3150 will amount to $3276 at a simple interest of 2% per annum?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
(6) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.