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So I'm doing a little financial planning, and I'm looking into the worthwhile-ness of paying off my student loans as quickly as possible. Being that I have multiple student loans, I combined them all together in a weighted average, putting me at around $30,000 with a 4.5% annual interest rate, which I believe compounds daily. (numbers rounded for simplicity)

I can very easily figure out if I pay PMT amount per month, how long it will take me to pay off given no interest:

CV / PMT = M

Where CV is Current Value, PMT is payment per month, and M is months spent paying off. But this is not very useful to me.

I can also sort of figure out if interest is simple, and doesn't compound:

Daily Interest = CV*R/365 Corrected Daily Interest = (Daily Interest/2)

CV / PMT-(CDI*30) = M

Corrected Daily Interest means that, assuming a linear decline in current value, the accrued interest at a daily rate will be on average, the Initial Balance divided by two. It makes sense to me and I think it checks out, but I could be horribly wrong.

Given this, I can also solve for total accrued interest over the payoff time.

M*30*CDI = TI

Where TI = Total Interest.

But this isn't accurate enough, because I know how brutal compound interest can be, which is what is the case here. I'd like to include that in my calculations, but most formulas I seem to find only solve for Months to Pay Off, or Future Value, but I'm trying to figure out both, and do it in a way I can put it into an excel formula. Any guidance would be great!

I've been trying to use this site for help.

yathern
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  • Amortization is hard to calculate by hand, that's why there are calculators online. You've given the principal and interest, but not the length of the loan or the payment amounts, so there isn't enough information to help you. As a general guideline, you are paying 0.045*30K=1350 in the first year in interest, less with a smaller principal. – vadim123 Apr 16 '16 at 18:50
  • Goggle for 'mortgage calculator' on the web, these are apps which can provide a table of payments, interest and outstanding balance. You can do the calculation yourself, it involves the geometric series and you'll have to numerically solve the sum at the end, kinda tedious. Oh - look at this one - http://loanlane.com/amort_sched.php - cheers. – user247608 Apr 16 '16 at 18:52
  • Thanks vadim123. The loan length is 120 months, but isn't that the maximum? I'm trying to figure out where I stand if I pay double the minimum monthly amount. How much does my total interest change, etc. – yathern Apr 16 '16 at 19:19

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