A business is paying off a debt by paying an installment 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 installment and there remain 15 further installments of $8000 and a final repayment of $5000 at the end of the 16th year.
The Attempt at a Solution
Originally I thought this to be a future value problem but I realized it was a present value problem. I used the Present value annuity equation:
P.V.=[(1-(1+i)^-n)/i]*R, where R=8000
Where i is 0.055 and n=15
This gave me a present annuity factor of 10.0375... which was then multiplied by 8000 to give $80300.64. Then I believe because this is annuity due it has to be multiplied by 1+i, which gives $84717.18. Then the last payment of $5000 has to be made. This should have interest calculated on it shouldn't it? If so then it is $5275. This should be subtracted from the value found. This gives $79442.18. The answer is $82423.55 apparently. So where did I go wrong?