Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $8700
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$8700 = P (1 + 4% × 5)
⇒ $8700 = P (1 + 4/100 × 5)
⇒ $8700 = P (1 + 4 × 5/100)
⇒ $8700 = P (1 + 20/100)
⇒ $8700 = P (100 + 20/100)
⇒ $8700 = P × 120/100
⇒ P × 120/100 = $8700
⇒ P = 8700/120/100
⇒ P = 8700 × 100/120
⇒ P = 8700 × 100/120
⇒ P = 870000/120
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 8700, then the Principal = 100/120 × 8700
= 100 × 8700/120
= 870000/120
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(4) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(6) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(10) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.