Kalpna opened this portfolio 4 years ago.

Question

- A $8500 fund that earns 5.45%, compounded annually
- Monthly deposits of $200 into an account earning 3%, compounded monthly

a) What will be the portfolio's value in 30 years when Kalpna is ready to retire?
b) What will be the portfolio's rate of return?

Answer 1

So I will assume a total time of 34 years or 408 months

amount 30 years from now
= 8500(1.0545)^34 + 200( 1.0025^408 - 1)/.0025
= 51641.968 + 141573.33655
= $ 193215.33

b) is quite complicated.
Let the monthly return be i

then 8500(1+12i)^34 + 200( (1+i)^408 - 1)/i = 193215.33

I entered
solve 8500(1+12x)^34 + 200( (1+x)^408 - 1)/x = 193215.33
into Wolfram and exceeded the standard computation time.

(notice I changed the i to x, since Wolfram interprets i as √-1, the standard definition of i )

Answer 2

ahhh, just tried it again without the "solve"

http://www.wolframalpha.com/input/?i=8500%281%2B12x%29%5E34+%2B+200%28+%281%2Bx%29%5E408+-+1%29%2Fx+%3D+193215.33

and got
x = .0031041
or
i = .0031041
12i = .0372492

So the equivalent annual rate of return for his portfolio is
3.725 %

check:
8500(1.03725)^34 + 200(1.0031041^408 - 1)/.0031041
=193216.61
I am off by $1.28 , due to rounding off my decimals