Question:
If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3564
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
$3564 = P (1 + 2% × 4)
⇒ $3564 = P (1 + 2/100 × 4)
⇒ $3564 = P (1 + 2 × 4/100)
⇒ $3564 = P (1 + 8/100)
⇒ $3564 = P (100 + 8/100)
⇒ $3564 = P × 108/100
⇒ P × 108/100 = $3564
⇒ P = 3564/108/100
⇒ P = 3564 × 100/108
⇒ P = 3564 × 100/108
⇒ P = 356400/108
⇒ 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 = 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 3564, then the Principal = 100/108 × 3564
= 100 × 3564/108
= 356400/108
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(3) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(6) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.