A 20-year annuity of forty $7,000 semiannual payments will begin 10 years from now, with the first payment coming 10.5 years from now. a. If the discount rate is 11 percent compounded monthly, what is the value of this annuity 4 years from now?

The value after 4 years = $59,079.75

Explanation:

To calculate the value of the annuity in four years from now

we first calculate the Present value of the annuity pretending we are at the beginning of the payment year

Pv = C[1-1 / (1+r) ^t]/r

c = $7,000

r = 11% / 2 = 0.055

t = 20 * 2 = 40

Pv = 112,322.87

Then we make the Pv in 10 years the total amount the investment

A = P (1+r) ^t

A = 112,322.87

r = 0.055

t = 10*2 = 20

P = 38496.30

After getting the Principal amount of the investment then we can get the value after 4 years making

n = 4*2 = 8

A = $59079.75