Answer:
The present worth of this investment = -$31,204.78
Explanation:
Note: See the attached excel file for the calculation of the present worth of this investment (in bold red color).
In the attached excel file, the following are used:
Loan from bank = Purchase price * (1 / 4) = $130,000 * (1 / 4) = $32,500
Initial cost = Purchase price - Loan from bank = $130,000 - $32,500 = $97,500
The annual required equal loan payments is calculated using the formula for calculating loan amortization as follows:
P = (A * (r * (1 + r)^n)) / (((1 + r)^n) - 1) .................................... (1)
Where,
P = Annual required equal loan payment = ?
A = Loan amount from bank = $32,500
r = interest rate = 12%, or 0.12
n = number of payment years = 3
Substituting all the figures into equation (1), we have:
P = Annual required equal loan payment = ($32,500 * (0.12 * (1 + 0.12)^3)) / (((1 + 0.12)^3) - 1) = $13,531.34
From the attached excl file, the present worth of this investment is equal to -$31,204.78
