Question:
If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3600
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
$3600 = P (1 + 5% × 4)
⇒ $3600 = P (1 + 5/100 × 4)
⇒ $3600 = P (1 + 5 × 4/100)
⇒ $3600 = P (1 + 20/100)
⇒ $3600 = P (100 + 20/100)
⇒ $3600 = P × 120/100
⇒ P × 120/100 = $3600
⇒ P = 3600/120/100
⇒ P = 3600 × 100/120
⇒ P = 3600 × 100/120
⇒ P = 360000/120
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3600, then the Principal = 100/120 × 3600
= 100 × 3600/120
= 360000/120
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.