Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $9060
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$9060 = P (1 + 4% × 5)
⇒ $9060 = P (1 + 4/100 × 5)
⇒ $9060 = P (1 + 4 × 5/100)
⇒ $9060 = P (1 + 20/100)
⇒ $9060 = P (100 + 20/100)
⇒ $9060 = P × 120/100
⇒ P × 120/100 = $9060
⇒ P = 9060/120/100
⇒ P = 9060 × 100/120
⇒ P = 9060 × 100/120
⇒ P = 906000/120
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 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 9060, then the Principal = 100/120 × 9060
= 100 × 9060/120
= 906000/120
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(4) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.