Question:
Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3651.5
Rate of Simple Interest (R) = 3%
Time (T) = 3 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
$3651.5 = P (1 + 3% × 3)
⇒ $3651.5 = P (1 + 3/100 × 3)
⇒ $3651.5 = P (1 + 3 × 3/100)
⇒ $3651.5 = P (1 + 9/100)
⇒ $3651.5 = P (100 + 9/100)
⇒ $3651.5 = P × 109/100
⇒ P × 109/100 = $3651.5
⇒ P = 3651.5/109/100
⇒ P = 3651.5 × 100/109
⇒ P = 3651.5 × 100/109
⇒ P = 365150/109
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 3651.5, then the Principal = 100/109 × 3651.5
= 100 × 3651.5/109
= 365150/109
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(5) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(9) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.