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 6% simple interest for 8 years.
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(3) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?