Question:
If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4920
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
$4920 = P (1 + 5% × 4)
⇒ $4920 = P (1 + 5/100 × 4)
⇒ $4920 = P (1 + 5 × 4/100)
⇒ $4920 = P (1 + 20/100)
⇒ $4920 = P (100 + 20/100)
⇒ $4920 = P × 120/100
⇒ P × 120/100 = $4920
⇒ P = 4920/120/100
⇒ P = 4920 × 100/120
⇒ P = 4920 × 100/120
⇒ P = 492000/120
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4920, then the Principal = 100/120 × 4920
= 100 × 4920/120
= 492000/120
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(3) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(9) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?