Xavier deposits $6 daily into an interest bearing account to save money for renovations to his bathroom. The account earns 4.57%which compounds annually. What is the present value of the investment if Xavier renovates his bathroom in 5 years?

Question

Xavier deposits $6 daily into an interest bearing account to save money for renovations to his bathroom.  The account earns 4.57%which compounds annually.  What is the present value of the investment if Xavier renovates his bathroom in 5 years?

dumbcow · Answer

are we assuming 365 days in a yr ?

dumbcow · Answer

the yearly investment is 6*365 = 2190
the present value equation is:
$$PV = 2190(v +v^{2}+v^{3}+v^{4}+v^{5})$$
where
$$v = \frac{1}{1+i} = \frac{1}{1.0457}$$

dumbcow · Answer

using formula for sum of geometric series
$$PV = 2190(\frac{v(1-v^{5})}{1-v})$$

dumbcow · Answer

does this make sense at all ?? here is solution: http://www.wolframalpha.com/input/?i=p%3D2190*v%281-v%5E5%29%2F%281-v%29+%2C+v+%3D+1%2F1.0457

anonymous · Answer

im guessing 6(1.0457)^5

anonymous · Answer

Thank you so much.  The formula I had was 2190(1/.0457-1/1.0457)^5 and I was not getting anything close to the answer choices.  You guys rock!