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) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(4) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(9) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?