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) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(6) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
(9) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.