Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $7877.5
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
$7877.5 = P (1 + 3% × 5)
⇒ $7877.5 = P (1 + 3/100 × 5)
⇒ $7877.5 = P (1 + 3 × 5/100)
⇒ $7877.5 = P (1 + 15/100)
⇒ $7877.5 = P (100 + 15/100)
⇒ $7877.5 = P × 115/100
⇒ P × 115/100 = $7877.5
⇒ P = 7877.5/115/100
⇒ P = 7877.5 × 100/115
⇒ P = 7877.5 × 100/115
⇒ P = 787750/115
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 7877.5, then the Principal = 100/115 × 7877.5
= 100 × 7877.5/115
= 787750/115
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(3) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(5) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.