Question

A 20-year annuity of forty $5,000 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now.

a. If the discount rate is 11 percent compounded monthly, what is the value of this annuity 5 years from now?

b. What is the current value of the annuity?

Answer 1

EAR for 6 Months = (1+r)^n - 1

r = Int rate per month

n - 6 Months

= ( 1 + 0.009167)^6 - 1

= (1.009167^6) - 1

= 1.0563 - 1

= 0.0563 i.e 5.63%

PV of annuity after 10 Years:

Particulars	Amount
Cash Flow	$      5,000.00
Int Rate	5.63%
Periods	40

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r

= $ 5000 * [ 1 - [(1+0.0563)^-40]] /0.0563

= $ 5000 * [ 1 - [(1.0563)^-40]] /0.0563

= $ 5000 * [ 1 - [0.1118]] /0.0563

= $ 5000 * [0.8882]] /0.0563

$                78,879.46

Part A:

Price after 5 years = Price after 11 Years * PVF(r%, n)

r = 5.63%

n - 12

Price after 5 years = Price after 11 Years * PVF(r%, n)

= $ 78879.46 * PVF ( 5.63% , 12)
= $ 78879.46 * 0.5183

= $ 40880.54

Part B:

Price Today =   Price after 10 Years * PVF(r%, n)

r = 5.63%

n - 22

= $ 78879.46 * PVF ( 5.63% , 22)
= $ 78879.46 * 0.2997

= $ 23639.8

Pls do rate, if the answer is correct and comment, if any further assistance is required