Question:
If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3886
Rate of Simple Interest (R) = 4%
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
$3886 = P (1 + 4% × 4)
⇒ $3886 = P (1 + 4/100 × 4)
⇒ $3886 = P (1 + 4 × 4/100)
⇒ $3886 = P (1 + 16/100)
⇒ $3886 = P (100 + 16/100)
⇒ $3886 = P × 116/100
⇒ P × 116/100 = $3886
⇒ P = 3886/116/100
⇒ P = 3886 × 100/116
⇒ P = 3886 × 100/116
⇒ P = 388600/116
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 3886, then the Principal = 100/116 × 3886
= 100 × 3886/116
= 388600/116
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(2) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(4) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?