Help me calculate the interest in this problem

[danesh]

Can any onesolve this problem:

An investor deposit $1000 a year into a retirement account. Treat these deposits as a continuous income stream. If the money in the account earns 12% interest, compound continuously, how much money will be in the account after 8 years?

 

[tantoun2004]

Re: Compund interest

Hi,
I think you can solve it as follows:
*Get the effective interest rate i = exp(.12)-1
*Future worth after 8 years = 1000 (F/A,i,8)
where A=Annumal worth =1000
i=effective interest rate that you got from eqn above
(F/A,i,8) is the factor you can get from tables or by interpolation
Hope that this will help,
Reagrds,

Added after 2 minutes:

I'm sorry in typing but I'm not expert ...
I meant :[F/A,i,n] where n=8
Reagrds,

 

[rkodaira]

Re: Compund interest

Hi !

If you have a HP12C financial calculator (or another calculator) you will find:

g BEG
PMT = 1000 (periodic payments or deposits)
i = 12 (interest rate in %) or 12% per annum
n = 8 (number of periods)
FV = 13775.66 (future value)

If you do not have a financial calculator The formula is:

FV = PMT * (1+ i) * [(1 + i)^n - 1] / i (i in decimal format, so i = 0.12)

You can use also the Excel function:

=FV(interest rate;n periods;payments;present value;type)
=FV(12%;8;1000;0;1)
=13775.66

I am considering you deposit the payments in the beginning of each period and in one payment of 1000 each period.

If you have 12 payments of 1000/12 a year, the value is different
The interest rate will be 0.9489% per month
Number of periods will be 12 * 8 = 96
The future value will be:
VF = 13085.33