An investor purchases an annuity that will pay a constant payment starting today of $100. Beginning with the payment 12 years from today each payment will be 5% greater than the previous payment. The last payment will be received 25 years from today. The annuity is bought to yield an effective interest rate of i such that (vi)^4 = 0.85.
A. What is the purchase price of the annuity today?

present value = $1921.62

Explanation:

given data

payment = $100

rate g = 5 %

time = 12 year

solution

we get here interest rate that is

v =     .............1

0.85 =  

i = - 1

i = 4.14 %

now we get here present value of annuity that is

present value of annuity = payment × × (1+i)   .................2

put here value

present value of annuity = 100 ×     × ( 1 + 4.14 % )

present value of annuity = $969.15

and here present value of growing annuity that is

present value of growing annuity =   ............3

present value of growing annuity =

present value of growing annuity = $1489.16

so now we get

present value that is

present value = present value of annuity + present value of growing annuity .............4

present value = 969.15 +  

present value = $1921.62

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