Question:
Anthony had to pay $4945 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
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4945
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
$4945 = P (1 + 5% × 3)
⇒ $4945 = P (1 + 5/100 × 3)
⇒ $4945 = P (1 + 5 × 3/100)
⇒ $4945 = P (1 + 15/100)
⇒ $4945 = P (100 + 15/100)
⇒ $4945 = P × 115/100
⇒ P × 115/100 = $4945
⇒ P = 4945/115/100
⇒ P = 4945 × 100/115
⇒ P = 4945 × 100/115
⇒ P = 494500/115
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 4945, then the Principal = 100/115 × 4945
= 100 × 4945/115
= 494500/115
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(8) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?