# Finding present value

• Oct 26th 2008, 07:42 AM
dc52789
Finding present value
A $50 U.S. Savings Bond paying 6.22% compounded monthly matures in 11 years 2 months. What is the present value of the bond? • Oct 26th 2008, 07:55 AM Jhevon Quote: Originally Posted by dc52789 A$50 U.S. Savings Bond paying 6.22% compounded monthly matures in 11 years 2 months. What is the present value of the bond?

the formula for the present value, $P$, is given by

$P = \frac F{(1 + r)^n}$

where $F$ is the future value of the money, in this case, the value at maturity, $r$ is the interest rate in decimal form, and $n$ is the number of years it will take to get to $F$, which in this case, is $\frac {67}6 \approx 11.167$.

now to find $F$, use the regular compound interest formula, then plug it into the formula above to find the present value
• Oct 26th 2008, 08:03 AM
dc52789
Quote:

Originally Posted by Jhevon
the formula for the present value, $P$, is given by

$P = \frac F{(1 + r)^n}$

where $F$ is the future value of the money, in this case, the value at maturity, $r$ is the interest rate in decimal form, and $n$ is the number of years it will take to get to $F$, which in this case, is $\frac {67}6 \approx 11.167$.

now to find $F$, use the regular compound interest formula, then plug it into the formula above to find the present value

I don't get all that and I have no idea how you get 67/6.
• Oct 26th 2008, 08:07 AM
Jhevon
Quote:

Originally Posted by dc52789
I don't get all that and I have no idea how you get 67/6.

what i gave you are definitions. and the 67/6 is 11 years and 2 months. this is 11 years and 2/12 years, which is 67/2 years if you add those fractions, or 11.167 years.

the formula for P is the present value, which is what you are after. and i told you what the pieces of the formula are. so just find them one by one. r and n were given, now find F as directed
• Oct 26th 2008, 08:19 AM
dc52789
Quote:

Originally Posted by Jhevon
what i gave you are definitions. and the 67/6 is 11 years and 2 months. this is 11 years and 2/12 years, which is 67/2 years if you add those fractions, or 11.167 years.

the formula for P is the present value, which is what you are after. and i told you what the pieces of the formula are. so just find them one by one. r and n were given, now find F as directed

Um...I got 25 as my answer. is it correct?
• Oct 26th 2008, 08:44 AM
Jhevon
Quote:

Originally Posted by dc52789
Um...I got 25 as my answer. is it correct?

nope, using 3 decimal places, i got $50.95 it should be close to the principal, but a little bigger, unless you're losing money, which we're not what did you get for F? • Oct 26th 2008, 08:49 AM dc52789 Quote: Originally Posted by Jhevon nope, using 3 decimal places, i got$50.95

it should be close to the principal, but a little bigger, unless you're losing money, which we're not

what did you get for F?

I don't know how you get that.
So...
n = 12
r = .0622
t = 11.167
I don't know which one the $50 go to. • Oct 26th 2008, 08:54 AM Jhevon Quote: Originally Posted by dc52789 I don't know how you get that. So... n = 12 r = .0622 t = 11.167 I don't know which one the$50 go to.

the 50 is the P (principal) in the compound interest formula
• Oct 26th 2008, 09:10 AM
dc52789
Quote:

Originally Posted by Jhevon
the 50 is the P (principal) in the compound interest formula

I did that and still got 25
I did it like this
50(1+(0.0622/12))^(-12x11.167)
• Oct 26th 2008, 09:20 AM
Jhevon
Quote:

Originally Posted by dc52789
I did that and still got 25
I did it like this
50(1+(0.0622/12))^(-12x11.167)

using that same formula, without the minus sign, i get 99.96 for that. use that as F in the first formula i gave
• Oct 26th 2008, 09:31 AM
dc52789
Quote:

Originally Posted by Jhevon

using that same formula, without the minus sign, i get 99.96 for that. use that as F in the first formula i gave

then, the answer would be 48.46
• Oct 26th 2008, 09:48 AM
Jhevon
Quote:

Originally Posted by dc52789
then, the answer would be 48.46

what exactly are you doing?

i double checked and got the same answer as last time. i think you're probably plugging in things in your calculator wrong
• Oct 26th 2008, 09:56 AM
dc52789
Quote:

Originally Posted by Jhevon
what exactly are you doing?

i double checked and got the same answer as last time. i think you're probably plugging in things in your calculator wrong

This is what I did.
99.96/(1+0.0622)^12 = 48.46
• Oct 26th 2008, 10:00 AM
Jhevon
Quote:

Originally Posted by dc52789
This is what I did.
99.96/(1+0.0622)^12 = 48.46

in the present value formula, n is the number of years, not the number of times it is compounded. you should have 11.167, not 12
• Nov 5th 2008, 09:11 PM
dc52789
Quote:

Originally Posted by Jhevon
in the present value formula, n is the number of years, not the number of times it is compounded. you should have 11.167, not 12

I just realized that this may not be the right answer. There's no way the answer could be \$50.95.