Question:
Daniel had to pay $4715 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
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4715
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
$4715 = P (1 + 5% × 3)
⇒ $4715 = P (1 + 5/100 × 3)
⇒ $4715 = P (1 + 5 × 3/100)
⇒ $4715 = P (1 + 15/100)
⇒ $4715 = P (100 + 15/100)
⇒ $4715 = P × 115/100
⇒ P × 115/100 = $4715
⇒ P = 4715/115/100
⇒ P = 4715 × 100/115
⇒ P = 4715 × 100/115
⇒ P = 471500/115
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4715, then the Principal = 100/115 × 4715
= 100 × 4715/115
= 471500/115
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(9) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?