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 February 2nd, 2013, 09:13 AM #1 Member   Joined: Jun 2012 Posts: 64 Thanks: 0 Find the present value Find the present value of an annuity certain of $12000 p.a. payable monthly in arrear for 20 years when the rate of interest is 5% p.a. for the first 10 years and thereafter 2.5% per half year. [Ans:$152 783.23] I am unsure with what to do with the "2.5% per half year" part. I am approaching this problem with complex annuities but I keep getting an amount few thousand off. I think my problem lies in the 2.5%. Please help, thanks. February 2nd, 2013, 11:30 AM   #2
Math Team

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Re: Find the present value

Quote:
 Originally Posted by Keroro Find the present value of an annuity certain of $12000 p.a. payable monthly in arrear for 20 years when the rate of interest is 5% p.a. for the first 10 years and thereafter 2.5% per half year. [Ans:$152 783.23] I am unsure with what to do with the "2.5% per half year" part. I am approaching this problem with complex annuities but I keep getting an amount few thousand off. I think my problem lies in the 2.5%. Please help, thanks.
P = 1000, n=120 (months)

Step 1: calculate the present value as at 10th year of the monthly annuity of $1000 payable over the next 10 years @ 2.5 semi-annually. Rate needs to be converted to monthly equivalent (to match payment frequency): (1 + i)^12 = (1 + .025)^2 ..... i = .0041239.... PV1 = P[1 - 1/(1 + i)^n] / i : that'll give you 94504.618... (required value after 10 years) Step 2: calculate present value of above as of today. Rate must be converted again, to the monthly equivalent of 5% p.a.: (1 + i)^12 = 1.05 ..... i = .0040741.... PV2 = 94504.618 / (1 + i)^n = 58017.638... Step 3:calculate the present value as of today of the monthly annuity of$1000 payable
over the next 10 years @ 5% p.a.
We use the rate above: i = .0040741...
PV3 = P[1 - 1/(1 + i)^n] / i : that'll give you 94765.591...

So net PV = PV2 + PV3 = 58017.638... + 94765.591... = 152783.229....

It'll all look like this (bank statement basis):
Code:
MTH   PAYMENT     INTEREST      BALANCE
0                              152,783.23 : PV2 + PV3
1    -1,000.00      622.46     152,405.69
...
119  -1,000.00      390.01      95,117.09
120  -1,000.00      387.53      94,504.62 : see PV1
121  -1,000.00      390.01      93,894.35 : new rate 2.5% s.a. starts
...
239  -1,000.00        8.20         995.89
240  -1,000.00        4.11            .00
You're lucky the Ottawa Senators are not playing hockey this afternoon! February 3rd, 2013, 05:15 AM #3 Member   Joined: Jun 2012 Posts: 64 Thanks: 0 Re: Find the present value Thanks a lot of helping out! I've managed to solve this using complex annuities and actuarial science symbols. Do you have a program that prints out bank statements?  February 3rd, 2013, 11:19 AM   #4
Math Team

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Posts: 14,597
Thanks: 1039

Re: Find the present value

Quote:
 Originally Posted by Keroro Thanks a lot of helping out! I've managed to solve this using complex annuities and actuarial science symbols.
Yikes...why? All you need is 2 basic financial formulas as I've shown on my post...
If you didn't "follow", then what is your intent? Simply get an answer you can "copy"?

Quote:
 Do you have a program that prints out bank statements? "Bank statement printing" is more a routine than a program:
all it is is print the transactions in some fancy manner...

Anyhow, here's my program that fully handles your problem:
[square brackets show results or information]
p = 1000 : n = 120

i = 1.05^(1/12) - 1 [converted annual rate = .0040741...]
j = 1.025^(1/6) - 1 [converted s.a. rate = .0041239...]

pv1 = p*(1 - 1/(1 + j)^n / j [94504.618...]
pv2 = pv1 / (1 + i)^n [58017.638...]
pv3 = p*(1 - 1/(1 + i)^n / i [94765.591...]

b = pv2 + pv3 [balance in account at start = 152783.228...]

Following does the bank statement printing (m = month):

loop m from 1 to 240
if m = 121 then i = j [use s.a. rate from month 121]
k = b * i [interest for current month]
b = b - p + k [resulting account balance for current month]

print m, -p, k, b [current month's transaction printed]
endloop

That's it...if you TRY to understand it, you'll see there's no mystery nowhere  February 24th, 2013, 10:05 AM #5 Member   Joined: Jun 2012 Posts: 64 Thanks: 0 Re: Find the present value Ah thanks a lot! That's some hectic programming!  Tags find, present Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post marmozetka Algebra 3 May 21st, 2013 05:21 PM gouhayashi Economics 5 May 19th, 2011 10:39 PM Sandy123 Economics 1 October 6th, 2009 08:16 PM tbl9301 Economics 2 September 8th, 2009 03:54 PM simplequestion Economics 3 October 8th, 2008 01:41 PM

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