*Advance Algebra With Financial Applications*
[Work Is Shown]

Garrett has an annuity that pays $2,460 at the beginning of each year. If the economy grows at a rate of 2.35% semiannually, what is the value of the annuity if he received it in a lump sum now rather than over a period of nine years?

$40,168.22

$39,701.72

$20,084.11

$19,850.86
--------
FV = 2460((1+0.0235/2)^(2*9) - 1 )/( 0.0235/2 )

Question

*Advance Algebra With Financial Applications*
[Work Is Shown]

Garrett has an annuity that pays $2,460 at the beginning of each year. If the economy grows at a rate of 2.35% semiannually, what is the value of the annuity if he received it in a lump sum now rather than over a period of nine years?

 $40,168.22

 $39,701.72

 $20,084.11

 $19,850.86
--------
FV = 2460((1+0.0235/2)^(2*9) - 1 )/( 0.0235/2 )

amistre64 · Answer

present value of an annuity due

amistre64 · Answer

how do we interpret:  grows at a rate of 2.35% semiannually

anonymous · Answer

divide or time it by 2 ?

amistre64 · Answer

if you receive money know; and money in a year from now ... the intermediary rates are moot;  all that matters is the yearly rates i believe

amistre64 · Answer

2.35 doubled is 4.70 by the next year

PV of B now is B
PV of B beginning of year is 2.35  before the increase
PV of B beginning of 2years is 2.35+4.70  before the increase
PV of B beginning of 3years is 2.35+2(4.70)  before the increase

etc

does that make sense?

amistre64 · Answer

$$B/r_0+B/r_1+B/r_2+...+B/r_9=Present~value$$

amistre64 · Answer

excel would be useful for this :)

anonymous · Answer

but is there an easier formula

amistre64 · Answer

not really; which is why excel is useful.  i got no idea how to work a financial calculator with that stuff

amistre64 · Answer

am i interpreting the growth rate correctly?

anonymous · Answer

was mine ok ? FV = 2460((1+0.0235/2)^(2*9) - 1 )/( 0.0235/2 )

amistre64 · Answer

i cant say ....  looks like it has the parts ... but im not sure how youre interpreting the groath rate is a /2

anonymous · Answer

2.35% semiannually <---- 0.235*2 ?

amistre64 · Answer

it gets bumped up 2 times a year by .0235 ... and since our payments are at the start of the year. that would amount to a Payment of 2460 that is .0470 less than what it was worth a year before

amistre64 · Answer

the first year being .0235 less then that year before

amistre64 · Answer

0:  B0 = 2460(1)
1:  B1  = B0 (1-.0235)
2:  B2  = B1 (1-.0470)
3:  B3  = B2 (1-.0470)
...

is this right?

anonymous · Answer

I think so

amistre64 · Answer

then the sum of those values i get to about 20430 with an excel run

amistre64 · Answer

i cant be sure of it tho wince i have some doubts as to my interpretation of the information

anonymous · Answer

do you know the answer ?

anonymous · Answer

I never have trouble with these questions before .

amistre64 · Answer

im not sure what the answer would be at the moment no

what answer do you get?

anonymous · Answer

20,084.11

anonymous · Answer

wild guess

anonymous · Answer

@amistre64 dont waist your time , thank's alot for your time :D . I'm going to head to tutoring later for this lesson

amistre64 · Answer

what troubling me is:

Present value is defined as the amount of money you would have to invest at todays interest rates to get the value of the Future amount.

We are not given a present day interest rate to calculate this with.

2460 = PV(1+i)^n.   

PV = 2460/(1+i)^n

This does not account for inflation (economic growth rate)

the Present value of a sum of Future money adjusted for inflation is similar, but uses the inflation rate:

PV = 2460/(1+g)^n

Since no current interest rate is available to determine what i think is a valid definition of Present Value .... Does this just imply that the sum totals due to inflation only?