Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8085
Rate of Simple Interest (R) = 2%
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
$8085 = P (1 + 2% × 5)
⇒ $8085 = P (1 + 2/100 × 5)
⇒ $8085 = P (1 + 2 × 5/100)
⇒ $8085 = P (1 + 10/100)
⇒ $8085 = P (100 + 10/100)
⇒ $8085 = P × 110/100
⇒ P × 110/100 = $8085
⇒ P = 8085/110/100
⇒ P = 8085 × 100/110
⇒ P = 8085 × 100/110
⇒ P = 808500/110
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8085, then the Principal = 100/110 × 8085
= 100 × 8085/110
= 808500/110
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(5) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(9) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.