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) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(9) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 4% simple interest?