After purchasing the apartment, Seth receives a street, sewer, and gutter assessment for $12,500 due in 2 years. How much would he have to invest today in a CD paying 2%, compounded semiannually, to fully pay the assessment in 2 years?
$12,500 x 2 = confused about the rest.
See previous post: Mon, 2-29-16, 2:12 AM.
P = Po(1+r)^n.
r = (2%/2)/100% = 0.01 = Semiannual % rate expressed as a decimal.
n = 2Comp./yr. * 2yrs = 4 Compounding peri0ds.
P = Po*(1.01)^4 = 12,500.
Po = ?.
To find out how much Seth would have to invest today in a CD to fully pay the assessment in 2 years, we need to calculate the present value of the $12,500.
The formula to calculate the present value of a future amount is:
PV = FV / (1 + r/n)^(n*t)
Where:
PV is the present value
FV is the future value
r is the annual interest rate
n is the number of times the interest is compounded per year
t is the number of years
In this case, the future value (FV) is $12,500, the annual interest rate (r) is 2%, the interest is compounded semiannually (n = 2), and the number of years (t) is 2.
Plugging these values into the formula, we have:
PV = 12,500 / (1 + 0.02/2)^(2*2)
First, let's simplify the formula inside the parentheses:
PV = 12,500 / (1 + 0.01)^(4)
Next, let's calculate the value inside the parentheses:
PV = 12,500 / (1.01)^4
PV = 12,500 / 1.04060401
Finally, let's calculate the present value:
PV = $11,978.58
Therefore, Seth would need to invest approximately $11,978.58 today in a CD paying 2%, compounded semiannually, to fully pay the assessment in 2 years.