Question

Your son is born today and you want to make him a millionaire by the time he is 50 years old. You deposit $50,000 in an investment account and want to know what annual interest rate must you earn in order to have the account value equal to $1,000,000 on your son's 50 th birthday.

Answer 1

Answer:

$1000000= 50000 (1+ \frac{i}{1})^{1*50}$

$20 = (1+i)^{50}$

$20^{1/50} = 1+i$

$i = 20^{1/50} -1 = 0.0617$

And if we convert this into % we got $i = APR = 6.17 \%$

See explanation below.

Explanation:

We assume that we have compounding interest.

For this case we can use the future value formula given by:

$FV= PV (1+\frac{i}{n})^{nt}$

Where:

FV represent the future value desired = 1000000

PV= represent the present value = 50000

i = the interest rate that we desire to find in fraction

n = number of times that the interest rate is compounding in 1 year, since the rate is annual then n=1

t = represent the number of years= 50 years

So then we have everything in order to replace and we got:

$1000000= 50000 (1+ \frac{i}{1})^{1*50}$

Now we can solve for the interest rate i like this:

$20 = (1+i)^{50}$

$20^{1/50} = 1+i$

$i = 20^{1/50} -1 = 0.0617$

And if we convert this into % we got $i = APR = 6.17 \%$