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) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.