Question:
If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $4968
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
$4968 = P (1 + 2% × 4)
⇒ $4968 = P (1 + 2/100 × 4)
⇒ $4968 = P (1 + 2 × 4/100)
⇒ $4968 = P (1 + 8/100)
⇒ $4968 = P (100 + 8/100)
⇒ $4968 = P × 108/100
⇒ P × 108/100 = $4968
⇒ P = 4968/108/100
⇒ P = 4968 × 100/108
⇒ P = 4968 × 100/108
⇒ P = 496800/108
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 4968, then the Principal = 100/108 × 4968
= 100 × 4968/108
= 496800/108
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(8) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?