Question

Problem 6-4 Calculating Annuity Present Value [LO1] An investment offers $6,400 per year for 15 years, with the first payment occurring on year from now. If the required return is 6 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g. 32.16.) Present value What would the value be if the payments occurred for 40 years? (Do intermediate calculations and round your final answer to 2 decimal places, e.g 32.16.) not round Present value What would the value be if the payments occurred for 75 years? (Do not r intermediate calculations and round your final answer to 2 decimal places, e 32.16.) .g., Present value What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Present value

Answer 1

Part (a)
Formula for calculating value of investment
Present value of annuity =			Annuity amount *   [ 1 - {1/((1+r)^n) ] / r
No. of years =		15
Annuity payments =		6400
Interest rate (r ) =		6%
Present value of investment = 6400 * [ 1 - {1/ (1 +0.06)^15} ] / 0.06
Value of investment at 6% =			$62,158.39
So, Value of investment is $62158.39.
Part (b)
No. of years =		40
Annuity payments =		6400
Interest rate (r ) =		6%
Present value of investment = 6400 * [ 1 - {1/ (1 +0.06)^40} ] / 0.06
Value of investment at 6% =			$96,296.30
So, Value of investment is $96,296.30.
Part (c )
No. of years =		75
Annuity payments =		6400
Interest rate (r ) =		6%
Present value of investment = 6400 * [ 1 - {1/ (1 +0.06)^75} ] / 0.06
Value of investment at 6% =			$1,05,317.43
So, Value of investment is $105,317.43.
Part (d)
Annuity payments =		6400
Interest rate (r ) =		6%
For forever, Perpetuity formula is = Annuity amount / Interest rate
	6400/6%
	$1,06,666.67
So, Value of investment is $106,666.67