Question:
If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $4032
Rate of Simple Interest (R) = 3%
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
$4032 = P (1 + 3% × 4)
⇒ $4032 = P (1 + 3/100 × 4)
⇒ $4032 = P (1 + 3 × 4/100)
⇒ $4032 = P (1 + 12/100)
⇒ $4032 = P (100 + 12/100)
⇒ $4032 = P × 112/100
⇒ P × 112/100 = $4032
⇒ P = 4032/112/100
⇒ P = 4032 × 100/112
⇒ P = 4032 × 100/112
⇒ P = 403200/112
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4032, then the Principal = 100/112 × 4032
= 100 × 4032/112
= 403200/112
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.