Question

To save for her newborn son's college education, lea wilson will invest $1,000 at the beginning of each year for the next 18 years. the interest rate is 12 percent. what is the future value? use appendix

c.

Answer 1

You need to use this statement:

`Fn =P(1+r)^n`
where:
P- the amount of initial capital
Fn - final capital after n-years
r- annual effective interest rate
n-number of years

Generally we need to put $1000 for the next 18 years so this statement looks like this:


`F_(n-1) =P(1+r)^n^-^1`
and the last invest

`F_(1)=P(1+r)^1`

So we need to add all years of capital

`S=F_(n)+F_(n-1) + F_(n-2) + ... + F_(2)+F_(1)`


`S=P(1+r)^n + P(1+r)^2+...+P(1+r)^n^-^2 +P(1+r)^n^-^1`
`+P(1+r)^n`

And finally we get this statement:

`S=P(1+r) ((1+r)^n-1)/((1+r)-1)`

and after all put values we get:


`S=1000 ((1+0,12)^1^8-1)/((1+0,12)-1) =55749,71`$

I don't know what value of tax you have so it is gross value. You need to sybtract tax from this received value