# Math Help - future value of an ordinary simple annuity

1. ## 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 2. 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 3. i must have forgotten to bracket the exponent ( 12 * 5 ) thanks for pointing that out. But still the 2nd option is unclear 4. 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. 5. 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
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.

6. 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?

7. 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? )

8. 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
Add 'em up: ~87,060

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

No. 10 000 ( 1 + 0.075/12)^60

> 1000 [ 1 - ( 1 + 0.075/12)^-60 / 0.075 ] = 90 745.58 ( mistake? )

Sorry; typed PV formula (but used FV; 72,527 is correct):
FV = 1000[(1 + i)^n - 1)] / i
= 1000[(1 + .075/12)^60 - 1)] / (.075/12) = ~72,527
.