Question:
If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5580
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
$5580 = P (1 + 5% × 4)
⇒ $5580 = P (1 + 5/100 × 4)
⇒ $5580 = P (1 + 5 × 4/100)
⇒ $5580 = P (1 + 20/100)
⇒ $5580 = P (100 + 20/100)
⇒ $5580 = P × 120/100
⇒ P × 120/100 = $5580
⇒ P = 5580/120/100
⇒ P = 5580 × 100/120
⇒ P = 5580 × 100/120
⇒ P = 558000/120
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5580, then the Principal = 100/120 × 5580
= 100 × 5580/120
= 558000/120
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(7) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(10) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.