Question:
If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4582
Rate of Simple Interest (R) = 4%
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
$4582 = P (1 + 4% × 4)
⇒ $4582 = P (1 + 4/100 × 4)
⇒ $4582 = P (1 + 4 × 4/100)
⇒ $4582 = P (1 + 16/100)
⇒ $4582 = P (100 + 16/100)
⇒ $4582 = P × 116/100
⇒ P × 116/100 = $4582
⇒ P = 4582/116/100
⇒ P = 4582 × 100/116
⇒ P = 4582 × 100/116
⇒ P = 458200/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4582, then the Principal = 100/116 × 4582
= 100 × 4582/116
= 458200/116
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(5) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(7) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.