> Present value situation?

Present value situation?

Posted at: 2014-12-05 
For a growing annuity...where * is multiplying...

PV = PMT * { [ 1 - (1 + g / 1 + r)^n ] / (r - g) }

=4,000 * { [1 - (1.06 / 1.095)^10 ] / (0.095 - 0.06)) }

= 4,000 * { (1 - 0.72263) / 0.035 }

= 4,000 * 7.92479

= $31,699.14834, round to $31,699.15

or (rearranged)... PV =[ PMT / (r - g) ] * [ 1 - (1 + g / 1 + r)^n ]

= [4,000 / 0.035] * [1 - (1.06 / 1.095)^10 ]

= 114,285.7143 * 0.27737

= 31,699.14835

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RE Present value situation?

My problem: You are left an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $4000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments?

Answer choices: a) $31,699.15 b) $36,666.67 c) $41,121.21 d) $43,464.12 e) $46,908.17

I've tried a few different methods. One was to find annuity due for 10 years using Excel: =fv(.06,10,-4000), then discount that amount to present value with =pv(.095,10,0, amount).

Anyone know how to set this up?

Present value problems involving annuities, there are four variables:

(1) present value of an ordinary annuity or present value of an annuity due

(2) the amount of each annuity payment,

(3) the number of periods,

(4) the interest rate,

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My problem: You are left an inheritance that will provide an annual income for the next 10 years. You will receive the first payment one year from now in the amount of $4000. Every year after that, the payment amount will increase by 6 percent. What is your inheritance worth to you today if you can earn 9.5 percent on your investments?

Answer choices: a) $31,699.15 b) $36,666.67 c) $41,121.21 d) $43,464.12 e) $46,908.17

I've tried a few different methods. One was to find annuity due for 10 years using Excel: =fv(.06,10,-4000), then discount that amount to present value with =pv(.095,10,0, amount).

Anyone know how to set this up?