Question:
If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5820
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
$5820 = P (1 + 5% × 4)
⇒ $5820 = P (1 + 5/100 × 4)
⇒ $5820 = P (1 + 5 × 4/100)
⇒ $5820 = P (1 + 20/100)
⇒ $5820 = P (100 + 20/100)
⇒ $5820 = P × 120/100
⇒ P × 120/100 = $5820
⇒ P = 5820/120/100
⇒ P = 5820 × 100/120
⇒ P = 5820 × 100/120
⇒ P = 582000/120
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 5820, then the Principal = 100/120 × 5820
= 100 × 5820/120
= 582000/120
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(6) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.