Question:
If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3900
Rate of Simple Interest (R) = 5%
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
$3900 = P (1 + 5% × 4)
⇒ $3900 = P (1 + 5/100 × 4)
⇒ $3900 = P (1 + 5 × 4/100)
⇒ $3900 = P (1 + 20/100)
⇒ $3900 = P (100 + 20/100)
⇒ $3900 = P × 120/100
⇒ P × 120/100 = $3900
⇒ P = 3900/120/100
⇒ P = 3900 × 100/120
⇒ P = 3900 × 100/120
⇒ P = 390000/120
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 3900, then the Principal = 100/120 × 3900
= 100 × 3900/120
= 390000/120
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.