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The Big Three Plus One => General Chat => Topic started by: Matt-Cook1 on May 20, 2009, 08:26:00 am

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 20, 2009, 08:26:00 am

Doing up some code to figure out the best strategy for repaying my student loan, but i'm not from a strong finance background and there's something i'm not sure of.

I want to observe the viability of various monthly repayments, from 100 bucks per month up to 2000 bucks per months (constant over the length of the loan).

- The loan is compounded annually
- There is an additional monthly repayment which is a function of salary. (Prob irrelevant to problem).
- I've assumed salary to multiply by a factor each year (s_rate > 1). (Prob irrelevant to problem).
- Repayments above 500 get a 10% bonus. (Prob irrelevant to problem).

So after some calculations, for all repayment inputs, it shows how much more than the principal I have paid. eg if principal was 100000, it'll say for some monthly repayment "you paid 110000", and for a slower repayment, it might say "you paid 111000".
-----
My question, and I believe it may be a a simple one, but the complexity of the loan/repayment scheme confuses me! :

In calculating the present day value of the interest paid on the loan (for each repayment amount), is it fair to just use the difference between the initial loan amount and the total amount paid.

eg:
initial loan = 100000
months to repay = 50
total amount paid = 110000
difference = 10000
bank interest rate (monthly) = 0.0035
present value = 10000 / ((1 + 0.0035)^50)

I think what confuses me is that the 10000 accumulates over the length of the loan, it's not just some value that suddenly appears 50 months from now, warranting a simple FV to PV conversion.... OR IS IT? Also that the "total amount paid" has no reference to a time and I haven't assigned it a time-based value.

Ok sorry this was long winded but it'd be great to get some insight. Cheers!

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 20, 2009, 08:50:00 am

Perhaps the thing to do is calculate present value of interest added each time the loan is compounded, and the sum of them is the correct present value? gah so convoluted.

Title: Someone please answer this finance question ?
Post by: Lovins on May 20, 2009, 10:07:00 am

I'm a bit rusty on this stuff (couldn't really helped you about 6 months ago) but do you mean 1. you pay monthly, principal only, and interest is calculated on the balance at the end of the year and you pay a year's worth of interest then? or 2. you pay monthly, principal only, but interest is compounded each month, and you pay the 12 months total interest at the end of the year?

 

If 1, then is .0035 a nominal or effective monthly rate? (i.e. is the yearly rate 1.0035^12 or 1 + .0035*12 )

 

I'm confused since you gave # months and a monthly interest rate, but say the loan is compounded annually, and also choice (2) corresponds to a loan compounded monthly, which is how you (correctly) calculated PV of interest. Well, you're correct only if it's really compounded monthly.

Also I'm not sure why you're interested in PV of interest, unless you're looking to make an investment at that same rate to finance the total interest paid at the end of 50 months; although interest is paid throughout the life of the loan, not all at the end.

Title: Someone please answer this finance question ?
Post by: Scrambler Fanny on May 20, 2009, 02:06:00 pm

English or GTFO!!!

Title: Someone please answer this finance question ?
Post by: RWG on May 20, 2009, 02:31:00 pm

Who has student loans? Have you people never heard of parents or the military?

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 21, 2009, 08:06:00 am

One thing: The loan is from the government, it has a 2.8 % p.a. rate. The 0.0035 is monthly interest rate for commercial banks.



Lovins said:

"I'm a bit rusty on this stuff (couldn't really helped you about 6 months ago) but do you mean 1. you pay monthly, principal only, and interest is calculated on the balance at the end of the year and you pay a year's worth of interest then? or 2. you pay monthly, principal only, but interest is compounded each month, and you pay the 12 months total interest at the end of the year?

If 1, then is .0035 a nominal or effective monthly rate? (i.e. is the yearly rate 1.0035^12 or 1 + .0035*12 )"

- I pay a fixed amount every month. Loan interest is compounded at the end of each year (2.8% p.a. , the 0.0035 is the monthly rate for the commercial banks, not the loan). I don't pay off the loan interest at a particular time, I just keep putting in an amount each month until the balance is zero.

- The yearly rate for the bank is 4.35 % ( = (1+0.0035)^12 - 1)



"I'm confused since you gave # months and a monthly interest rate, but say the loan is compounded annually, and also choice (2) corresponds to a loan compounded monthly, which is how you (correctly) calculated PV of interest. Well, you're correct only if it's really compounded monthly. "

So I used a monthly bank interest rate to calculate the present value of the interest accumulated by the loan. But yes, the loan is compounded annually (at the government loan interest rate, 2.8%)




"Also I'm not sure why you're interested in PV of interest, unless you're looking to make an investment at that same rate to finance the total interest paid at the end of 50 months; although interest is paid throughout the life of the loan, not all at the end."


I want to compare the present value for the accumulated interests for different rates of monthly repayment. Then I want to compare those to what a different investment would accumulate to. Perhaps it is best, for example to pay off the loan slow and invest more, versus paying the loan off fast and investing less.




So I suppose my question boils down to : If a loan starts at P dollars, and is paid (in any arbitrary fashion) by time t, having paid a total of (P + I) dollars, how does one evaluate the present value of the extra amount paid (interest), I. Can we simply use the FV -> PV conversion formula, using I, t and a commercial bank interest rate?


Thanks ed

Title: Someone please answer this finance question ?
Post by: Red Bull on May 21, 2009, 08:11:00 am

I think you need a program for that (Excel Solver or any other) or use a trial and error process. Mathematically not really possible to determine an interest rate in the PV of several payments in the future.

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 21, 2009, 08:20:00 am

As long as I know what to do I can program it (https://forums.the-elite.net/proxy.php?request=http%3A%2F%2Fwww.ezboard.com%2Fintl%2Faenglish%2Fimages%2Femoticons%2Fsmile.gif&hash=1adea417e08e9042f9ce1a5426616bf29f2ca20e)

Title: Someone please answer this finance question ?
Post by: Lovins on May 21, 2009, 09:23:00 am

Quote from: Red Bull

I think you need a program for that (Excel Solver or any other) or use a trial and error process. Mathematically not really possible to determine an interest   rate in the PV of several payments in the future.

He already has his interest rate, no need to solve for it (regardless, you can always solve for i if you have N (# payments), loan amount, and payment amount).

Matt, given what you said now, it sounds to me like you had it right all along. Once you figure out total interest paid on the loan, based on the loan (government) rate, simply convert that to PV as you did, using the bank rate.

As for comparing strategies, the more you pay each month (resulting in less # of payments) the less the interest you'll ultimately pay, and the less you'll have to invest, and vice-versa. But you probably knew that already.

Let me know if that clears everything up.

Title: Someone please answer this finance question ?
Post by: Red Bull on May 21, 2009, 10:32:00 am

It's because I really don't understand the question properly (https://forums.the-elite.net/proxy.php?request=http%3A%2F%2Fwww.ezboard.com%2Fintl%2Faenglish%2Fimages%2Femoticons%2Ftongue.gif&hash=7cfc888ebd66cf455a55fd5e124ee8267da91148)

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 22, 2009, 04:51:00 am

Thanks Ed! Yeah just wasn't sure if using the total time from loan start to loan paid off was allowed. Somehow convinced myself that I might actually have to progressively calculate and sum PV of interest each time it was added on.

Just FYI, the main reason I want to simulate this stuff is because the interest rate for the loan is lower than the bank interest rate (meaning you'd be best to pay it off as slow as the government lets you whilst letting your money earn in the bank / other investment), but you get a 10% bonus on repayments over 500, which adds some uncertainty to it. Fast or slow we'll find out!

RB is teh big cutie (https://forums.the-elite.net/proxy.php?request=http%3A%2F%2Fwww.ezboard.com%2Fintl%2Faenglish%2Fimages%2Femoticons%2Fsmile.gif&hash=1adea417e08e9042f9ce1a5426616bf29f2ca20e)

Title: Someone please answer this finance question ?
Post by: Your Eliteness on May 22, 2009, 10:52:00 am

I'm a nut about this sort of stuff.

I've made my own little PHP application which:
a) downloads my transactions from my online bank (after logging in manually)
b) graphs the balances of my accounts over time
c) predicts future interest, repayments and savings and graphs that
d) calculates what my ideal sell price is in order to make the entire house-buying worthwhile, and graphs that over time

My method for solving your problem would be to make a script which loops through each month and adds repayments, calculating and delivering interest where appropriate, until the loan is completely repaid. Looks like you're all sorted though.

Title: Someone please answer this finance question ?
Post by: Matt-Cook1 on May 22, 2009, 09:00:00 pm

Sounds pretty sweet Ryan. My data retrieval skills are pretty low. I'd like to be able to do step a.

Just because i'm very highly open to coding practice criticism, having only learned to code as an engineer, I'll smack the code up here and some IT guys can throw some comments at me if they want.

Just ignore this geek stuff though prob:

clc, clear, format short g

june = 2; %how many months from now is june? (HECS increases)
january = 9; %how many months from now is january? (Salary increases)

H_ini = XXXXXXX;
extra_goes = 'HECS';

R = 0.028; %Multiplier for unpaid HELP each year

west.y = 0.0435;
west.m = (1 + west.y)^(1/12) - 1;

%Preallocate
monthly_extras = 0:10:10000;
interest = zeros(1,length(monthly_extras));
months = zeros(1,length(monthly_extras));
H = H_ini*ones(1,length(monthly_extras)); %Amount owed to gov.
years = zeros(1,length(monthly_extras));
total_months = zeros(1,length(monthly_extras));

for i = 1:length(monthly_extras);
   
    %reset for each one.
    s = XXXXXX; %Salary in Dollars relative to HELP
    s12 = s/12; %salary per month
    s_rate = 1.2; %rate at which salary increases every year
    repay_rate = calc_repay_rate(s);
   
    if monthly_extras(i) >= 500
        bonus = 0.1;
    else
        bonus = 0;
    end
   
    while H(i) > 0
       
        months(i) = months(i) + 1;
       
        %Salary increase
        if mod(months(i),12) == january
            s = s*s_rate;
            s12 = s/12; %salary per month
            repay_rate = calc_repay_rate(s);
        end
       
        %HECS accumulates interest
        if mod(months(i),12) == june;
            H(i) = H(i) + H(i)*R;
            interest(i) = interest(i) + H(i)*R;
        end
       
        %compulsory repayment from salary
        H(i) = H(i) - s12*repay_rate;
       
        %Optional repayment
        if strcmp(extra_goes,'HECS')
            H(i) = H(i) - monthly_extras(i)*(1 + bonus);
        end
       
    end
   
    %H might go below zero. No need.
    years(i) = months(i)/12;
   
end

PV = interest ./ (1 + west.m).^months;