Question:
Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4816
Rate of Simple Interest (R) = 4%
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
$4816 = P (1 + 4% × 3)
⇒ $4816 = P (1 + 4/100 × 3)
⇒ $4816 = P (1 + 4 × 3/100)
⇒ $4816 = P (1 + 12/100)
⇒ $4816 = P (100 + 12/100)
⇒ $4816 = P × 112/100
⇒ P × 112/100 = $4816
⇒ P = 4816/112/100
⇒ P = 4816 × 100/112
⇒ P = 4816 × 100/112
⇒ P = 481600/112
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4816, then the Principal = 100/112 × 4816
= 100 × 4816/112
= 481600/112
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(3) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(8) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.