Question:
If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $4320
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
$4320 = P (1 + 5% × 4)
⇒ $4320 = P (1 + 5/100 × 4)
⇒ $4320 = P (1 + 5 × 4/100)
⇒ $4320 = P (1 + 20/100)
⇒ $4320 = P (100 + 20/100)
⇒ $4320 = P × 120/100
⇒ P × 120/100 = $4320
⇒ P = 4320/120/100
⇒ P = 4320 × 100/120
⇒ P = 4320 × 100/120
⇒ P = 432000/120
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 4320, then the Principal = 100/120 × 4320
= 100 × 4320/120
= 432000/120
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(4) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.