Question:
If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3720
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
$3720 = P (1 + 5% × 4)
⇒ $3720 = P (1 + 5/100 × 4)
⇒ $3720 = P (1 + 5 × 4/100)
⇒ $3720 = P (1 + 20/100)
⇒ $3720 = P (100 + 20/100)
⇒ $3720 = P × 120/100
⇒ P × 120/100 = $3720
⇒ P = 3720/120/100
⇒ P = 3720 × 100/120
⇒ P = 3720 × 100/120
⇒ P = 372000/120
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3720, then the Principal = 100/120 × 3720
= 100 × 3720/120
= 372000/120
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(3) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(5) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(9) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.