Question

you can afford monthly deposits of $210 into an account that pays 3.9% compounded monthly. how long will it be until you have 5800 to buy a boat?

Answer 1

5800 = 210(1-k^(n*12))/(1-k), k=1+.039/12

Answer 2

if we just let n be months, then there is no need for the n*12 bit

Answer 3

B = P(1-k^n)/(1-k)

B(1-k)/P = 1-k^n

k^n = 1- B(1-k)/P

n ln(k) = ln(1- B(1-k)/P)

n = ln(1- B(1-k)/P)/ln(k)

Answer 4

about 26 and a 1/2 months i believe

Answer 5

http://www.wolframalpha.com/input/?i=ln%281-5800%281-k%29%2F210%29%2Fln%28k%29%2C+k%3D1%2B.039%2F12

Answer 6

you are using sum of a geometric series amistre, right?

Answer 7

yes, and trying to determine if this would amount to an annuity due; i believe ive figured it for an ordinary annuity

Answer 8

thank you so much are you positive

Answer 9

im iffy, but fairly sure :)

Answer 10

m0 = 210
m1 = 210k + 210
m2 = 210k^2 + 210k + 210

mn = 210(geo sum)

Answer 11

do you get the same answer if youuse this calculator i found online http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

Answer 12

i typed things in and the calc isnt working idk

Answer 13

S = 1 + k + k^2 + k^n
-kS = -k -k^2 -k^n -k^(n+1)
------------------------------
S = (1 - k^(n+1))/(1-k)

Answer 14

i believe i am 1 month heavy

Answer 15

25 and a half months is what im wanting to go with ...

Answer 16

thats what the calc gave u?

Answer 17

no, thats what my own progression gave me

Answer 18

okay sweet can you just chek that link i sent to see if it matches because when i put it in it says that imj missing something idk if itll work for u to make sure that 25 and a half months is the right answer

Answer 19

youd have to put in a time period; say 4 years

Answer 20

well, 30 months to be certain, start it at 0

Answer 21

so youll see between 26 and 27 months the balance of 5800 slides in there

Answer 22

http://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

Answer 23

ohhh so idk if its 26 or 27

Answer 24

this is what i get for month 26 and 27
26 $ 210.00 $ 38.93 $ 11,260.00 $ 756.71 $ 12,016.71
27 $ 210.00 $ 39.74 $ 11,470.00 $ 796.45 $ 12,266.45

Answer 25

well, 26 is too short, so if you have to do months; bump it up to 27

Answer 26

okay thank u soooooooooo much

Answer 27

could you pleas ehelp me with another question please i am going to post it now

Answer 28

youre welcome; so i guess my 26 and a half would have been fine :)

Answer 29

ive got to move along at the moment

Answer 30

okay