Question:
If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3696
Rate of Simple Interest (R) = 3%
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
$3696 = P (1 + 3% × 4)
⇒ $3696 = P (1 + 3/100 × 4)
⇒ $3696 = P (1 + 3 × 4/100)
⇒ $3696 = P (1 + 12/100)
⇒ $3696 = P (100 + 12/100)
⇒ $3696 = P × 112/100
⇒ P × 112/100 = $3696
⇒ P = 3696/112/100
⇒ P = 3696 × 100/112
⇒ P = 3696 × 100/112
⇒ P = 369600/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3696, then the Principal = 100/112 × 3696
= 100 × 3696/112
= 369600/112
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(3) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(6) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.