Question:
If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4266
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
$4266 = P (1 + 2% × 4)
⇒ $4266 = P (1 + 2/100 × 4)
⇒ $4266 = P (1 + 2 × 4/100)
⇒ $4266 = P (1 + 8/100)
⇒ $4266 = P (100 + 8/100)
⇒ $4266 = P × 108/100
⇒ P × 108/100 = $4266
⇒ P = 4266/108/100
⇒ P = 4266 × 100/108
⇒ P = 4266 × 100/108
⇒ P = 426600/108
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4266, then the Principal = 100/108 × 4266
= 100 × 4266/108
= 426600/108
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(10) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.