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) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(5) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(9) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.