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 & 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) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?