Question:
If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5626
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
$5626 = P (1 + 4% × 4)
⇒ $5626 = P (1 + 4/100 × 4)
⇒ $5626 = P (1 + 4 × 4/100)
⇒ $5626 = P (1 + 16/100)
⇒ $5626 = P (100 + 16/100)
⇒ $5626 = P × 116/100
⇒ P × 116/100 = $5626
⇒ P = 5626/116/100
⇒ P = 5626 × 100/116
⇒ P = 5626 × 100/116
⇒ P = 562600/116
⇒ 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 = 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 5626, then the Principal = 100/116 × 5626
= 100 × 5626/116
= 562600/116
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(7) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(10) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.