Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $8970
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
$8970 = P (1 + 3% × 5)
⇒ $8970 = P (1 + 3/100 × 5)
⇒ $8970 = P (1 + 3 × 5/100)
⇒ $8970 = P (1 + 15/100)
⇒ $8970 = P (100 + 15/100)
⇒ $8970 = P × 115/100
⇒ P × 115/100 = $8970
⇒ P = 8970/115/100
⇒ P = 8970 × 100/115
⇒ P = 8970 × 100/115
⇒ P = 897000/115
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 8970, then the Principal = 100/115 × 8970
= 100 × 8970/115
= 897000/115
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(2) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(6) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.