$300,000 accumulated in 30 years @12% compounded annually. What would the sinking payment be?
amount = payment ( (1+i)^n - 1 )/i
sub in your values and solve for 'payment'
300000 = payment (1.12^30 - 1)/.12
2% on sale 60,000 4% on sale
60,000
sale 106,000
To calculate the sinking payment, we need to use the formula for the present value of an annuity. The sinking payment represents the equal periodic payments that occur over a specific period of time.
The formula for the present value of an annuity is:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value (the total amount accumulated)
P = Payment per period
r = Interest rate per period
n = Total number of periods
In this case:
PV = $300,000 (the total amount accumulated)
r = 12% per year (or 0.12)
n = 30 years
We need to solve the formula for P, which represents the sinking payment per period.
First, we can rearrange the formula to solve for P:
P = PV * (r / (1 - (1 + r)^(-n)))
Now let's substitute the given values:
P = $300,000 * (0.12 / (1 - (1 + 0.12)^(-30)))
Now we can calculate the sinking payment:
P = $300,000 * (0.12 / (1 - (1.12)^(-30)))
P ≈ $5,219.60
Therefore, the sinking payment would be approximately $5,219.60.