Answer:
7.54% and $308,000
Explanation:
Part 1 : Since, the amount formula in compound interest,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
P = principal value,
r = annual rate,
n = number of compounding periods in a year,
t = number of years,
If P = $ 50,000, n = 1,
[tex]A=50,000(1+r)^{t}-----(1)[/tex]
Suppose this amount is equivalent if [tex]\frac{r}{n}=0.037[/tex] and n = 2,
Then
[tex]50,000(1+0.037)^{2t}=50,000(1+r)^t[/tex]
[tex]1.037^2 = 1+ r[/tex]
[tex]1.075369-1 = r[/tex]
[tex]\implies r = 0.075369 = 7.5369\%\approx 7.54\%[/tex]
Hence, the equivalent annual growth rate for this investment would be 7.54%.
Part 2 :
If t = 25,
[tex]A= 50,000(1+0.075369 )^{25}=307544.40\approx \$ 308,000[/tex]
( Using calculator )
i.e. it would be worth $ 308,000( approx) after 25 years.
