Question

Suppose you have a goal of having a balance of $1000 in your investment account. No matter what your initial conditions or target value happen to be, are you always guaranteed to reach your goal within 15 years? If your answer is "no", find a combination of variables that will justify your answer.

Answer 1

My answer is "no".

The formula that is applicable in this case will be: Future value = present value*(1+r)^n

So $1,000 = present value*(1+r)^15

Now if present value is $500 then 1,000 should not be equal to 500*(1+r)^15. Now let 1000 = 500*(1+r)^15

Solving we get r = 4.73%. Thus r<4.73% in this case and if r<4.73% then balance will be less than $1,000.

The combination of variables that justifies my answer are:

Present value	r
50	<22.11%
100	<16.59%
150	<13.48%
200	<11.33%
250	<9.68%
300	<8.36%
350	<7.25%
400	<6.30%
450	<5.47%
500	<4.73%