Ed long promised to pay is son $400 semiannually for 12 years. Assume Ed can invest his money at 6 % in an ordinary annuity. How much must Ed invest today to pay his son $400 semiannually for 12 years?
i = .06/2 = .03
n = 24
Present value = 400(1 - 1.03^-24)/.03
= ....
you do the button-pushing
12 years x2 =24periods
6%/2=3%
24 periods @3%
400 x 16.9355= $6,774.20
To determine how much Ed must invest today, we need to calculate the present value of the annuity.
The formula to calculate the present value of an ordinary annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, the payment per period (semiannually) is $400, the interest rate is 6% (or 0.06 as a decimal), and the number of periods is 12 years, which translates to 24 semiannual periods.
Now let's plug in the values and calculate the present value:
PV = 400 * (1 - (1 + 0.06)^(-24)) / 0.06
Using a calculator or spreadsheet, the present value comes out to approximately $4,578.08.
Therefore, Ed must invest approximately $4,578.08 today to be able to pay his son $400 semiannually for 12 years.
To determine how much Ed must invest today, we can use the formula for the present value of an ordinary annuity.
The formula for the present value of an ordinary annuity is:
PV = PMT * [1 - (1+r)^(-n)] / r
Where:
PV = Present value (the amount Ed must invest today)
PMT = Payment (the amount Ed promises to pay his son semiannually, which is $400 in this case)
r = Interest rate per period (6% per annum, so we need it in semiannual terms, which is 3%)
n = Number of periods (12 years, so we multiply it by 2 since there are 2 semiannual periods within a year)
Now let's substitute the values into the formula and calculate:
PMT = $400
r = 3% or 0.03 (since it's a semiannual rate)
n = 12 years * 2 = 24 periods
PV = $400 * [1 - (1+0.03)^(-24)] / 0.03
Calculating this equation will give us the present value (PV) that Ed must invest today to pay his son $400 semiannually for 12 years.