Question:
Ashley had to pay $4959.5 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
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4959.5
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
$4959.5 = P (1 + 3% × 3)
⇒ $4959.5 = P (1 + 3/100 × 3)
⇒ $4959.5 = P (1 + 3 × 3/100)
⇒ $4959.5 = P (1 + 9/100)
⇒ $4959.5 = P (100 + 9/100)
⇒ $4959.5 = P × 109/100
⇒ P × 109/100 = $4959.5
⇒ P = 4959.5/109/100
⇒ P = 4959.5 × 100/109
⇒ P = 4959.5 × 100/109
⇒ P = 495950/109
⇒ 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 = 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 4959.5, then the Principal = 100/109 × 4959.5
= 100 × 4959.5/109
= 495950/109
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
(5) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.