Question:
If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5022
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
$5022 = P (1 + 2% × 4)
⇒ $5022 = P (1 + 2/100 × 4)
⇒ $5022 = P (1 + 2 × 4/100)
⇒ $5022 = P (1 + 8/100)
⇒ $5022 = P (100 + 8/100)
⇒ $5022 = P × 108/100
⇒ P × 108/100 = $5022
⇒ P = 5022/108/100
⇒ P = 5022 × 100/108
⇒ P = 5022 × 100/108
⇒ P = 502200/108
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5022, then the Principal = 100/108 × 5022
= 100 × 5022/108
= 502200/108
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(2) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(5) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(8) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.