Question:
If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5238
Rate of Simple Interest (R) = 2%
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
$5238 = P (1 + 2% × 4)
⇒ $5238 = P (1 + 2/100 × 4)
⇒ $5238 = P (1 + 2 × 4/100)
⇒ $5238 = P (1 + 8/100)
⇒ $5238 = P (100 + 8/100)
⇒ $5238 = P × 108/100
⇒ P × 108/100 = $5238
⇒ P = 5238/108/100
⇒ P = 5238 × 100/108
⇒ P = 5238 × 100/108
⇒ P = 523800/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5238, then the Principal = 100/108 × 5238
= 100 × 5238/108
= 523800/108
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(8) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?