Question

Will medal and fan!
What is the value of an annuity due at the end of 15 years of quarterly deposits of $2,000.00 with terms of 8 percent compounded quarterly?

Answer 1

Can someone please help with this?

Answer 2

I really just need help with how to deal with the 8% compounded quarterly

Answer 3

annuity due, is that the one at the begining or end of the month?

Answer 4

i spose ordinary is end, so annuity due starts with a payment

Answer 5

if we start with a balance of the first payment, and then add on payments for each compounding period, the formula i usually use turns to this
\[B_n=Pk^n+P\frac{k^n-1}{k-1}\]

Answer 6

i dont know what formula you use tho ....

Answer 7

i've never done a question like this one before

Answer 8

what types have you done?

Answer 9

how do you find the value of an ordinary annuity?

Answer 10

i've never worked with annuities before

Answer 11

well, what have you worked with?

Answer 12

Have you worked with loans yet?

Answer 13

monthly payments?

Answer 14

nope, i'm in a class and the very first thing is annuities

Answer 15

can you define what an annuity does? how would you explain it to someone?

Answer 16

an amount of money payed out at intervals?

Answer 17

yeah, so payments

Answer 18

lets say we pay ourself, we put money into an account that compounds the interest, quarterly

and each quarter we add more money .. if we do this for 15 years, how much money do we have saved up in the account?

this is the goal we are looking at

Answer 19

i start with amount P, and it compounds for 15*4 periods

i then add another P, that compounds for 15*4-1 periods

i then add another P, that compounds for 15*4-2 periods

i then add another P, that compounds for ....

i then add another P, that compounds for 0 periods,

i then look at the balance in my account

Answer 20

the only difference between an annuity due (starting with a payment) and an ordinary annuity (starting at 0) is that first payment that compounds for the full 15 years

Answer 21

but I spose you dont know how to add all that up do you

Answer 22

no not really
sorry

Answer 23

right, and thats why i provided my own formula, it puts the addition of all the payments into a nice neat format.

all i need from you is to tell me what it means to compound once a quarter, what is out interest adjustment?

Answer 24

what is **our interest adjustment

Answer 25

8% is a yearly interest amount, we dont compound in a year, but less then a year ... we compound 4 times a year. 8/4 = 2% each time

Answer 26

1.02 is out compounding rate for each period, and we have 15 years of 4 times a year = 60 periods in total

Answer 27

do you agree or disagree? any questions?

Answer 28

im good so far

Answer 29

so lets say k=1.02

P = 2000

B0 = P

B1 = Pk + P , money compounds and we add a payment

B2 = Pk^2 + Pk + P , money compounds and we add a payment

B3 = Pk^3 + Pk^2 + Pk + P , money compounds and we add a payment

this goes on and on and is a geometric series in k, which there is a nice formula for fining the sum of

\[B_n=Pk^n+P\underbrace{\frac{k^n-1}{k-1}}_{geo~series~sum}\]

Answer 30

i leave the first term where its at in my formula becasue the generally represents a starting balance that is different from P.

Answer 31

the ordinary annuity starts at a balance of 0, so the first term would be 0 in that case.

Answer 32

so, what is:

2000(1.02)^(60) + 2000((1.02)^(60)-1)/(.02)

Answer 33

234,665.14

Answer 34

thats what i get, so that is how much the annuity is worth, what is its present value?

Answer 35

FV = PV(1.02)^(60)

if we were to sell it today to an investor, they would pay us the present value of it or less for profit

Answer 36

234665/(1.02)^(60) = 71522 as a lump sum today for your annuity would have them break even. Its the amount of money they would have to put in the bank earning the same interest for the same time period

Answer 37

but my memory could be faded on that so dont worry to much about it

Answer 38

ok
i think i have the hang of this
i have another similiar question, would you be able to check it as I work through it to make sure im doing it right?