You can purchase a residential building lot for $60 000 cash or for $10 000 down and month-end payments of $1000 for five years. If money is worth 7.5% compounded monthly, which option should you chose?
i was part way to the answer when i encounterd a problem.
Using the formula FV= P ( 1 + r/n ) ^ n * t [for option 1]
where P = 60 000
t = 5
n = 12 60 000 ( 1 + 0.075/12 ) ^ 12 * 5
323 289.7797
for option 2 however ,
i'm confused on the same formula as suppose to a different one.
Different meaning FV = PMT [ 1 - ( 1 + i )^-n / i ]
i want to be abe to arrive at correct answer using
FV= P ( 1 + r/n ) ^ n * t
Many things we "WANT" are impossible!!
This formula: FV = PMT [{ 1 - ( 1 + i )^-n }/ i ] (notice extra brackets!)
MUST be used when dealing with payments (like your $1000 per month).
This formula: FV= PV ( 1 + i) ^ n
is used ONLY if there are no payments, but a Present Value (like your $60000).
i = .075/12, n = 60
Option 1:
60000(1 + i)^n = ~87,198
Option 2:
10000(1 + i)^n = ~14,533 (the 10,000 is treated same as the 60,000)
1000[{ 1 - ( 1 + i )^-n} / i ] = ~72,527
Add 'em up: ~87,060
Pretty close, hey?
By the way, were you TOLD to use Future Values?
Much faster/easier to use Present Values.
Option 2:
10000(1 + i)^n = ~14,533 (the 10,000 is treated same as the 60,000)
1000[{ 1 - ( 1 + i )^-n} / i ] = ~72,527
Add 'em up: ~87,060
10 000 ( 1 + 0.075/12)^12 = 10 776.33 ( mistake? )
1000 [ 1 - ( 1 + 0.075/12)^-60 / 0.075 ] = 90 745.58 ( mistake? )