Question:
If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $4020
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
$4020 = P (1 + 5% × 4)
⇒ $4020 = P (1 + 5/100 × 4)
⇒ $4020 = P (1 + 5 × 4/100)
⇒ $4020 = P (1 + 20/100)
⇒ $4020 = P (100 + 20/100)
⇒ $4020 = P × 120/100
⇒ P × 120/100 = $4020
⇒ P = 4020/120/100
⇒ P = 4020 × 100/120
⇒ P = 4020 × 100/120
⇒ P = 402000/120
⇒ 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 = 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 4020, then the Principal = 100/120 × 4020
= 100 × 4020/120
= 402000/120
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(6) 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.
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.