A business is paying off a debt by paying an instalment of $8000 at the end of each year. Interest is being charged at 5.5%. What is the outstanding debt if the business has just paid an instalment and there remain 15 further instalments of $8000 and a final repayment of $5000 at the end of the 16th year?

Question

anonymous · Answer

I've got up to finding that, at the end of the 15th year the value is $4739.34. I don't know how to use the annuity formulas to find the value of the debt.

anonymous · Answer

The textbook answer is $82 423.55. They don't specify whether they used an immediate or annuity due

ganeshie8 · Answer

So basically you need to find present value of 15 yearly installments of $8000 each
and one $5000 instalment

ganeshie8 · Answer

do you have present value of annuity formula ?

anonymous · Answer

I just got it! I found how long it would take for the $4739.34 to be paid off at the $8000 payments and then added that on to the 15 years. Sorry for wasting your time.

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=8000*%28%281-%281%2B0.055%29%5E%28-15%29%29%2F0.055%29

ganeshie8 · Answer

is that the present value for 15 installments of $8000 each ?

ganeshie8 · Answer

its okay, im also trying to review these

ganeshie8 · Answer

adding present value of "$5000 in 16 years" gives us http://www.wolframalpha.com/input/?i=8000*%28%281-%281%2B0.055%29%5E%28-15%29%29%2F0.055%29+%2B++5000%2F%281%2B0.055%29%5E16

anonymous · Answer

Yep, that's right

anonymous · Answer

Oh, wow, that is so much simpler that my way :P
Thanks for the help

anonymous · Answer

I thought there must be an easier way. I also understand how the formula actually works now, thanks

ganeshie8 · Answer

good to hear :)