Question:
Daniel had to pay $4592 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
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4592
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
$4592 = P (1 + 4% × 3)
⇒ $4592 = P (1 + 4/100 × 3)
⇒ $4592 = P (1 + 4 × 3/100)
⇒ $4592 = P (1 + 12/100)
⇒ $4592 = P (100 + 12/100)
⇒ $4592 = P × 112/100
⇒ P × 112/100 = $4592
⇒ P = 4592/112/100
⇒ P = 4592 × 100/112
⇒ P = 4592 × 100/112
⇒ P = 459200/112
⇒ 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 = 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 4592, then the Principal = 100/112 × 4592
= 100 × 4592/112
= 459200/112
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(2) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(8) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(10) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?