Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6435
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
$6435 = P (1 + 2% × 5)
⇒ $6435 = P (1 + 2/100 × 5)
⇒ $6435 = P (1 + 2 × 5/100)
⇒ $6435 = P (1 + 10/100)
⇒ $6435 = P (100 + 10/100)
⇒ $6435 = P × 110/100
⇒ P × 110/100 = $6435
⇒ P = 6435/110/100
⇒ P = 6435 × 100/110
⇒ P = 6435 × 100/110
⇒ P = 643500/110
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 6435, then the Principal = 100/110 × 6435
= 100 × 6435/110
= 643500/110
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(4) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(10) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.