Question:
If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5488
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$5488 = P (1 + 3% × 4)
⇒ $5488 = P (1 + 3/100 × 4)
⇒ $5488 = P (1 + 3 × 4/100)
⇒ $5488 = P (1 + 12/100)
⇒ $5488 = P (100 + 12/100)
⇒ $5488 = P × 112/100
⇒ P × 112/100 = $5488
⇒ P = 5488/112/100
⇒ P = 5488 × 100/112
⇒ P = 5488 × 100/112
⇒ P = 548800/112
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 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 5488, then the Principal = 100/112 × 5488
= 100 × 5488/112
= 548800/112
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(2) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.