Question:
If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4620
Rate of Simple Interest (R) = 5%
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
$4620 = P (1 + 5% × 4)
⇒ $4620 = P (1 + 5/100 × 4)
⇒ $4620 = P (1 + 5 × 4/100)
⇒ $4620 = P (1 + 20/100)
⇒ $4620 = P (100 + 20/100)
⇒ $4620 = P × 120/100
⇒ P × 120/100 = $4620
⇒ P = 4620/120/100
⇒ P = 4620 × 100/120
⇒ P = 4620 × 100/120
⇒ P = 462000/120
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4620, then the Principal = 100/120 × 4620
= 100 × 4620/120
= 462000/120
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(6) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(7) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?
(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?