How is the principal payment calculated before interest is addes if; P = 50,000
interest = 9% and compounded for 7 years
To calculate the principal payment before interest is added, we need to first understand the concept of compound interest and use the compound interest formula.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan/ investment
P = the principal amount (initial investment/loan)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $50,000, the interest rate (r) is 9%, and the term (t) is 7 years. However, we need to calculate the compound interest without the interest included.
To do this, we need to rearrange the compound interest formula to solve for P:
A = P(1 + r/n)^(nt)
Divide both sides by the compound factor:
A/(1 + r/n)^(nt) = P
Substituting the values:
P = 50,000/(1 + 0.09/1)^(1*7)
Now, calculate the principal payment by evaluating the formula:
P = 50,000/(1 + 0.09/1)^(1*7)
P = 50,000/(1 + 0.09)^(7)
P = 50,000/(1.09)^7
P ≈ $28,045.75
Therefore, the principal payment before interest is added is approximately $28,045.75.