Question:
If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3456
Rate of Simple Interest (R) = 2%
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
$3456 = P (1 + 2% × 4)
⇒ $3456 = P (1 + 2/100 × 4)
⇒ $3456 = P (1 + 2 × 4/100)
⇒ $3456 = P (1 + 8/100)
⇒ $3456 = P (100 + 8/100)
⇒ $3456 = P × 108/100
⇒ P × 108/100 = $3456
⇒ P = 3456/108/100
⇒ P = 3456 × 100/108
⇒ P = 3456 × 100/108
⇒ P = 345600/108
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3456, then the Principal = 100/108 × 3456
= 100 × 3456/108
= 345600/108
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(6) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.