Given the Following Assumption

Question

Given the following assumptions (principal = $700, APR compounded monthly = 3.50%, monthly payment = $60), suppose you invested for 30 years rather than just three, calculate your final balance to the nearest dollar.
 

a. $42,345

b. $39,345

c. $43,671

d. $40,122

e. $46,198

Answer 1

in 30 years there are 30*12 = 360 months
after the first month you have 700*(1 + .035) = 724.5 dollars but add in an additional 60 dollars so you have 784.5 dollars.

after the second month you have 784.5*(1.035) = 812 dollars plus the 60 dollar fee, so 872 dollars.

 

this becomes:

(700*1.035 + 60)*1.035 + 60

 

and you have to do this for all 360 months

 

Of course this becomes impractical so you use a formula with exponents that allows you to do all 360 months at once - you should find this link very helpful for both explaining the full equation and giving you an example to follow:

 

http://people.wku.edu/david.neal/116/Unit5/Annuities.pdf