Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9085
Rate of Simple Interest (R) = 3%
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
$9085 = P (1 + 3% × 5)
⇒ $9085 = P (1 + 3/100 × 5)
⇒ $9085 = P (1 + 3 × 5/100)
⇒ $9085 = P (1 + 15/100)
⇒ $9085 = P (100 + 15/100)
⇒ $9085 = P × 115/100
⇒ P × 115/100 = $9085
⇒ P = 9085/115/100
⇒ P = 9085 × 100/115
⇒ P = 9085 × 100/115
⇒ P = 908500/115
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 = 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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 9085, then the Principal = 100/115 × 9085
= 100 × 9085/115
= 908500/115
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(5) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(9) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.