brain

I'm trying to finish one of my time value of money projects and I can't seem to figure out how to do certain problems without utilizing the tables. If anyone can help me with this problem, I would be very grateful.

Q: You want to buy a house and need a $25,000 down payment. If you can earn 5% on your money and can save $6,000 a year, how long will it be before you have your downpayment?

The only way I could do this problem was as follows:
25000/6000 = 4.167 and I went to do tables to find the number, but it's not there. I can only get an approximate estimate which would be in a little under 4 years.

psycho-

You need to account interest (rfr or whatever) on the future values

__________________
Victor

psycho-

BTW

Correct number is = 3.870549446


Final part of the equation is 1.208= 1.05^n

You just use goalseek on excel if you like that type of stuff

Future value Equation itself was :

25000=6000[{(1.05)^n}-1]/.05

LegendKiller

Actually, you are coming up with an incorrect number.

To get the accurate amount of number of periods remaining you can use the nper function in excel, which gives you the exact number of periods remaining.

Your equation for FV of annuities is correct.

FVA = PMT(FVIFA)
FVIFA(future value interest factor for an annuity) =(((1+i)^n) - 1)/i

The correct solution is 3.87869.

LegendKiller

On a side note, if you cannot use excel and you do not have a fin calc you can find the value this way.


Take your future value / PMT

This yields your FVIA multiplier, which equals 4.166667 in this case.

Take that number and find the closest value on the tables that match the 5% IR you have.

Next subtract your 4.166667 from the lesser of the two n periods factors (4.166667-3.1525)= 1.014167. This gives you the difference in factors.

The last step is to take the delta factor and figure out what % it is of the difference between the two periods (3 and 4).

1.014167/ (4.3101 - 3.1252) = 3+.876094.


There is a difference between FVIA calculated by the Goalseek (or solver function on a TI-85) because the tables are rounded and this is an approximation. However, it is close enough that your professor should not care, if he does you can show him how you did this and he will give you your grade.

Merlin

What you want to do is find the future value of an annuity.

Use the following formula...


Where
Future Value = 25,000
Present Value = 0
Payment = 6,000
I = 5% or 0.05

You get

25,000 = 6,000*[{(1.05)^n-1}/0.05]
4.1667 = {(1.05)^n-1}/0.05
0.2083 = (1.05)^n-1
1.2083 = (1.05)^n
Therefore n = 3.8781

Pretty much the same answer as above just different due to rounding. Hope the actual formuls helps you understand it better.

And if you want to be a spiteful little jerk you can give him grief for not specifying if the $6,000 comes in at the beginning of the period or at the end.

__________________

DaFunkyUnit

shouldnt this be in the "Investments" forum?

__________________

LegendKiller

LOL Merlin, I didn't add in the part about beginning/end because it wasn't specified, but thats funny nontheless .


DF, it isn't in investments because it is dealing with a question from a text book.

If he were to come in here and ask "How do I invest my money so I can get 25k in 4 years" that would be different.

psycho-

Of course, goal seek is inherently inaccurate unless i run it. Nonetheless, I know I should've used nper. Amazingly,I waived out of finance classes for my grad school...I'm so used to doing it on paper in undergrad, so I never had excel training on this stuff.

LegendKiller

I guess your's is because I used it under mine and it worked perfectly and spit out the number nper did.


LK

brain

I'm cool up to this part. How do you solve for n from here? I don't fall within the Asian sterotype of being a math wiz.

coleslaw

Logs are your friend!

1.2083 = (1.05)^n
log 1.2083 = n log 1.05

Can you take it from there?

__________________
A priest, a paladin and Varimathras walk into a bar...