Question:
Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $5232.5
Rate of Simple Interest (R) = 5%
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
$5232.5 = P (1 + 5% × 3)
⇒ $5232.5 = P (1 + 5/100 × 3)
⇒ $5232.5 = P (1 + 5 × 3/100)
⇒ $5232.5 = P (1 + 15/100)
⇒ $5232.5 = P (100 + 15/100)
⇒ $5232.5 = P × 115/100
⇒ P × 115/100 = $5232.5
⇒ P = 5232.5/115/100
⇒ P = 5232.5 × 100/115
⇒ P = 5232.5 × 100/115
⇒ P = 523250/115
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 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 5232.5, then the Principal = 100/115 × 5232.5
= 100 × 5232.5/115
= 523250/115
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(7) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(9) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(10) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.