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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(2) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?
(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(8) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.