future value of an ordinary simple annuity

• Aug 9th 2009, 02:51 PM
diehardmath4
future value of an ordinary simple annuity
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
• Aug 9th 2009, 07:40 PM
Wilmer
Quote:

Originally Posted by diehardmath4
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

Don't you think that's a bit high; if I lend you \$60,000 will you
pay me back over \$323,000?

Should be:
60 000 ( 1 + 0.075/12 ) ^ (12 * 5)
= 60 000 ( 1 + 0.075/12 ) ^ 60 = ~87,198
• Aug 10th 2009, 04:35 AM
diehardmath4
i must have forgotten to bracket the exponent ( 12 * 5 ) thanks for pointing that out. But still the 2nd option is unclear
• Aug 10th 2009, 05:34 AM
diehardmath4
Actually This question isn't about lending money . It's about owning a condo and out of the two options which one is the better one.
• Aug 10th 2009, 05:39 AM
Wilmer
Quote:

Originally Posted by diehardmath4
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

Pretty close, hey?

By the way, were you TOLD to use Future Values?
Much faster/easier to use Present Values.
• Aug 10th 2009, 05:49 AM
Wilmer
Something else...but this is kind of "my way", so just a suggestion:

Take the PMT equation:
FV = PMT [{ 1 - ( 1 + i )^-n }/ i ]

Kinda confusing-looking, right?

FV = PMT(x / i) where x = 1 - ( 1 + i )^-n

Much easier to "see", right?
• Aug 10th 2009, 11:25 AM
diehardmath4
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

10 000 ( 1 + 0.075/12)^12 = 10 776.33 ( mistake? )

1000 [ 1 - ( 1 + 0.075/12)^-60 / 0.075 ] = 90 745.58 ( mistake? )
• Aug 10th 2009, 01:24 PM
Wilmer
Quote:

Originally Posted by diehardmath4
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