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 07-01-2012, 07:00 PM #1 adept     Join Date: Jan 2009 Posts: 776 Help with time value of money? Hey, just starting out with this topic and having a few problems, maybe some of you can help me out. What quarterly payment is necessary to accumulate \$1 million over 10 years if the annual percentage rate (APR) is 8 percent, compounded quarterly? Assume payments are made at the beginning of each quarter. I'm getting 1.02 as the effective quarterly rate. Is this right? Then all I have to do is calculate payment by using future value of annuity formula right?
 07-01-2012, 10:59 PM #2 Carpal \'Tunnel     Join Date: Jul 2010 Location: Quest for 12 Posts: 10,937 Re: Help with time value of money? I am getting \$15,096.35 Not 100% sure tho.
 07-01-2012, 11:43 PM #3 old hand     Join Date: Nov 2008 Location: NYC Posts: 1,690 Re: Help with time value of money? FVoa = PMT [((1 + i)^n - 1) / i] 1,000,000 / (((1.02^40)-1)/.02) = PMT PMT = 16,555.75
07-01-2012, 11:44 PM   #4
old hand

Join Date: May 2010
Location: GMU
Posts: 1,396
Re: Help with time value of money?

Quote:
 Originally Posted by MXdotCH Hey, just starting out with this topic and having a few problems, maybe some of you can help me out. What quarterly payment is necessary to accumulate \$1 million over 10 years if the annual percentage rate (APR) is 8 percent, compounded quarterly? Assume payments are made at the beginning of each quarter. I'm getting 1.02 as the effective quarterly rate. Is this right? Then all I have to do is calculate payment by using future value of annuity formula right?
Didn't do the calc but your set up is right.

 07-02-2012, 12:49 AM #5 Goes hard in the paint     Join Date: Aug 2008 Location: NY Posts: 7,404 Re: Help with time value of money? yeah its 16555.75 \$1,000,000 / Future value of an annuity @ 2% for 40 periods (60.402) pv table here in case you want to try a different rate
07-02-2012, 02:19 AM   #6
Pooh-Bah

Join Date: May 2006
Location: que, said che
Posts: 4,728
Re: Help with time value of money?

Quote:
 Originally Posted by MXdotCH ... if the annual percentage rate (APR) is 8 percent, compounded quarterly? ... I'm getting 1.02 as the effective quarterly rate. Is this right?
Not exactly 1.02 but should be close enough to get a decent number.

The effective quarterly rate would be 1.08^(1/4), so a sliver above 1.0194

 07-02-2012, 08:01 AM #7 old hand     Join Date: Nov 2008 Location: NYC Posts: 1,690 Re: Help with time value of money? the compounding factor is: 1 + 1/[(1+(r/n))^nt] n = number of times compounding t = periods in terms of quarters
 07-02-2012, 09:23 AM #8 Carpal \'Tunnel     Join Date: Dec 2006 Location: London Posts: 13,012 Re: Help with time value of money? Noob question, won't \$1m in 10 years have about the same purchasing power as \$500k today?
 07-02-2012, 09:40 AM #9 old hand     Join Date: Nov 2008 Location: NYC Posts: 1,690 Re: Help with time value of money? Gullanian: Depends on how you compound it and at what interest rate. You are basically saying, assuming annual compounding: 2 = (1+r)^10 ln2 = 10 ln(1+r) ln2 / 10 = ln (1+r) .0693 = ln (1+r) e^.0693 = 1+r r = 7.1758% In today's day, good luck finding 7.1758% interest rates.
07-02-2012, 10:44 AM   #10

Join Date: Jan 2009
Posts: 776
Re: Help with time value of money?

Quote:
 Originally Posted by The Financier the compounding factor is: 1 + 1/[(1+(r/n))^nt] n = number of times compounding t = periods in terms of quarters
I don't get what's the difference between n and t, sounds like the same thing. The textbook I use gives me a formula to find the effective rate for any period which is:

k = ( 1 + Quoted Rate/ M )^(m/f) - 1

where m= No. of times interest compounded per quoted period
and f= Number of sub periods in the quoted period

I guess its the same one you mentionned right? Isn't the interest compounded always as many times as the number of sub periods?

 07-02-2012, 10:55 AM #11 old hand     Join Date: Nov 2008 Location: NYC Posts: 1,690 Re: Help with time value of money? yes, it is the same thing. n = compounding in a year. t = years.
07-02-2012, 11:20 AM   #12

Join Date: Jan 2009
Posts: 776
Re: Help with time value of money?

Quote:
 Originally Posted by The Financier yes, it is the same thing. n = compounding in a year. t = years.
Is it simply t = years or years in terms of period?

And say I am given an nominal interest rate of 8% but for 2 years, t would be 2 or .5?

 07-02-2012, 01:00 PM #13 old hand     Join Date: Nov 2008 Location: NYC Posts: 1,690 Re: Help with time value of money? In my formula, you can see I raise it to the (nt) power. Using my definitions, which I think will cause less problems as you do these problems, equals the amount of periods. If you are given a nominal interest rate of 8% for 2 years, here are three examples: Annual compounding: (1 + .08/1)^2 Semi-annual: (1 + .08/2)^4 Quarterly: (1 + .08/4)^8 I use T = 2 in each of these examples, but the n changes depending on how many times you compound it.
 07-02-2012, 01:29 PM #14 grinder     Join Date: Feb 2007 Posts: 620 Re: Help with time value of money? I wish I used this forum when I took Finance
07-02-2012, 09:40 PM   #15
Pooh-Bah

Join Date: Mar 2010
Posts: 5,995
Re: Help with time value of money?

Quote:
 Originally Posted by auralex14 I wish I used this forum when I took Finance
Most homework problems threads are usually closed I think. Some of this stuff is still fun though.

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