Answer:
[tex] 1000000= 50000 (1+ \frac{i}{1})^{1*50}[/tex]
[tex] 20 = (1+i)^{50}[/tex]
[tex] 20^{1/50} = 1+i[/tex]
[tex] i = 20^{1/50} -1 = 0.0617[/tex]
And if we convert this into % we got [tex]i = APR = 6.17 \%[/tex]
See explanation below.
Explanation:
We assume that we have compounding interest.
For this case we can use the future value formula given by:
[tex] FV= PV (1+\frac{i}{n})^{nt}[/tex]
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:
[tex] 1000000= 50000 (1+ \frac{i}{1})^{1*50}[/tex]
Now we can solve for the interest rate i like this:
[tex] 20 = (1+i)^{50}[/tex]
[tex] 20^{1/50} = 1+i[/tex]
[tex] i = 20^{1/50} -1 = 0.0617[/tex]
And if we convert this into % we got [tex]i = APR = 6.17 \%[/tex]
