Question:
If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3780
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
$3780 = P (1 + 2% × 4)
⇒ $3780 = P (1 + 2/100 × 4)
⇒ $3780 = P (1 + 2 × 4/100)
⇒ $3780 = P (1 + 8/100)
⇒ $3780 = P (100 + 8/100)
⇒ $3780 = P × 108/100
⇒ P × 108/100 = $3780
⇒ P = 3780/108/100
⇒ P = 3780 × 100/108
⇒ P = 3780 × 100/108
⇒ P = 378000/108
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 3780, then the Principal = 100/108 × 3780
= 100 × 3780/108
= 378000/108
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(8) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.