Carl wants to have $1500 in the bank on Dec 15th. He plans to deposit an equal amount on the 15th of every month, Jan - July), into an account that pays 6% compunded monthly. Then, Carl will stop making payments but will leave the money in the same account. What should be the amount of each of the 7 montly payments? Can anyone help me workout this problem step by step? Thanks!
2007-03-12 19:00:43 · 4 answers · asked by no_idea 1 in Business & Finance ➔ Investing
$1500 is the future value that Carl will have in Dec. The question is asking how much the payments prior to that with interest etc so that he will end up with $1500 at the end of the year (Dec).
2007-03-12 19:23:18 · update #1
First you discount the 1500 back to July for a period of 5 months to check what is required by July 15th:
1,500 / (1.005)^5 = 1,463.06
Now you need to make 7 equal payments to get to this value at July 15th. In Excel you can do this by using the following formula:
=PMT(6%/12,7,,1,463.06)
This will give you a value of 205.89 that needs to be deposited for 7 months, Jan-Jul
2007-03-12 23:08:51 · answer #1 · answered by Cheanea 3 · 0⤊ 0⤋
I can help you with the compound interest table. The equal sum deposited is called an Annuity. So if x is the equal amount for seven months and 6% annual interest rate is 6/12 or 0.5% monthly.
Now the equation is,
x(Future value interest factor of an Annuity for 7 periods at 0.5%) = 1500/e^0.005x5.
Here the only unknown is x, the quantity in the bracke can be got from any compound interest table. Now it is one equation with one unknown and solve for x and you will get the monthly equal payment. x is the value of each of the 7 monthly payments you are looking for. I don't have a compound interest table handy so I let you do the answer yourselves. You won't be disappointed using this method.
2007-03-13 13:09:49 · answer #2 · answered by Mathew C 5 · 0⤊ 0⤋
Jan 15th He has $1500 + 0.5% x( 1500) + $1500
Feb 15Th he has the above + 0.5% (above) + $1500
Mar 15 he has Total as on Feb 15 + 0.5%(Feb 15) + $1500
Get the idea, Every month, the money that has been in for 30 days gets 0.5% (1/12 of 6%) added to it + add the $1500 deposit
Do this for all 30 day periods you want, if you don't add $1500. It is only the money in for 30 days that has 0.5% added to it.
2007-03-13 02:14:50 · answer #3 · answered by bob shark 7 · 0⤊ 0⤋
putting money in:
Balance = P(1 + r)^n + c[((1 + r)^n + 1 - (1 + r))/r]
P=principal
C=addition
^=power of as in 2^3=8
r= rate or interest
n=time
letting it sit
balance=P(1 + r)^n
I'm guessing
F(x)= the function P(1 + r)^n + c[((1 + r)^n + 1 - (1 + r))/r]
$1500 = F(x)(1 + r)^n
Solve for C
2007-03-13 03:33:52 · answer #4 · answered by gregory_dittman 7 · 0⤊ 0⤋