Question:
Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3657
Rate of Simple Interest (R) = 2%
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
$3657 = P (1 + 2% × 3)
⇒ $3657 = P (1 + 2/100 × 3)
⇒ $3657 = P (1 + 2 × 3/100)
⇒ $3657 = P (1 + 6/100)
⇒ $3657 = P (100 + 6/100)
⇒ $3657 = P × 106/100
⇒ P × 106/100 = $3657
⇒ P = 3657/106/100
⇒ P = 3657 × 100/106
⇒ P = 3657 × 100/106
⇒ P = 365700/106
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 = 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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3657, then the Principal = 100/106 × 3657
= 100 × 3657/106
= 365700/106
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(9) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?