Question:
If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5510
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
$5510 = P (1 + 4% × 4)
⇒ $5510 = P (1 + 4/100 × 4)
⇒ $5510 = P (1 + 4 × 4/100)
⇒ $5510 = P (1 + 16/100)
⇒ $5510 = P (100 + 16/100)
⇒ $5510 = P × 116/100
⇒ P × 116/100 = $5510
⇒ P = 5510/116/100
⇒ P = 5510 × 100/116
⇒ P = 5510 × 100/116
⇒ P = 551000/116
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5510, then the Principal = 100/116 × 5510
= 100 × 5510/116
= 551000/116
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?
(6) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.