Question:
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.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $5100
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
$5100 = P (1 + 5% × 4)
⇒ $5100 = P (1 + 5/100 × 4)
⇒ $5100 = P (1 + 5 × 4/100)
⇒ $5100 = P (1 + 20/100)
⇒ $5100 = P (100 + 20/100)
⇒ $5100 = P × 120/100
⇒ P × 120/100 = $5100
⇒ P = 5100/120/100
⇒ P = 5100 × 100/120
⇒ P = 5100 × 100/120
⇒ P = 510000/120
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 5100, then the Principal = 100/120 × 5100
= 100 × 5100/120
= 510000/120
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(5) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.