Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $8855
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
$8855 = P (1 + 3% × 5)
⇒ $8855 = P (1 + 3/100 × 5)
⇒ $8855 = P (1 + 3 × 5/100)
⇒ $8855 = P (1 + 15/100)
⇒ $8855 = P (100 + 15/100)
⇒ $8855 = P × 115/100
⇒ P × 115/100 = $8855
⇒ P = 8855/115/100
⇒ P = 8855 × 100/115
⇒ P = 8855 × 100/115
⇒ P = 885500/115
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 8855, then the Principal = 100/115 × 8855
= 100 × 8855/115
= 885500/115
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(2) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?