Question:
If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3840
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
$3840 = P (1 + 5% × 4)
⇒ $3840 = P (1 + 5/100 × 4)
⇒ $3840 = P (1 + 5 × 4/100)
⇒ $3840 = P (1 + 20/100)
⇒ $3840 = P (100 + 20/100)
⇒ $3840 = P × 120/100
⇒ P × 120/100 = $3840
⇒ P = 3840/120/100
⇒ P = 3840 × 100/120
⇒ P = 3840 × 100/120
⇒ P = 384000/120
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 3840, then the Principal = 100/120 × 3840
= 100 × 3840/120
= 384000/120
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(2) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(6) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.