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) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.