Question:
If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4680
Rate of Simple Interest (R) = 5%
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
$4680 = P (1 + 5% × 4)
⇒ $4680 = P (1 + 5/100 × 4)
⇒ $4680 = P (1 + 5 × 4/100)
⇒ $4680 = P (1 + 20/100)
⇒ $4680 = P (100 + 20/100)
⇒ $4680 = P × 120/100
⇒ P × 120/100 = $4680
⇒ P = 4680/120/100
⇒ P = 4680 × 100/120
⇒ P = 4680 × 100/120
⇒ P = 468000/120
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 = 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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4680, then the Principal = 100/120 × 4680
= 100 × 4680/120
= 468000/120
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(4) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.