Question:
If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3960
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
$3960 = P (1 + 5% × 4)
⇒ $3960 = P (1 + 5/100 × 4)
⇒ $3960 = P (1 + 5 × 4/100)
⇒ $3960 = P (1 + 20/100)
⇒ $3960 = P (100 + 20/100)
⇒ $3960 = P × 120/100
⇒ P × 120/100 = $3960
⇒ P = 3960/120/100
⇒ P = 3960 × 100/120
⇒ P = 3960 × 100/120
⇒ P = 396000/120
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3960, then the Principal = 100/120 × 3960
= 100 × 3960/120
= 396000/120
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(4) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(5) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(9) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?