Question:
How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8395
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
$8395 = P (1 + 3% × 5)
⇒ $8395 = P (1 + 3/100 × 5)
⇒ $8395 = P (1 + 3 × 5/100)
⇒ $8395 = P (1 + 15/100)
⇒ $8395 = P (100 + 15/100)
⇒ $8395 = P × 115/100
⇒ P × 115/100 = $8395
⇒ P = 8395/115/100
⇒ P = 8395 × 100/115
⇒ P = 8395 × 100/115
⇒ P = 839500/115
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 8395, then the Principal = 100/115 × 8395
= 100 × 8395/115
= 839500/115
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(4) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.