Question

In repayment of a loan today, Nicholas agreed to pay a financial institution $1,000 at the end of each month over a 3 year period. Assuming the interest rate on the loan is 8.5%, what is the loan amount if the first payment is made immediately?

Please tell me how to use a financial calculator to get the answer.  What is the difference between C/Y and P/Y in financial calculator? I type my way to calculate below.

2nd  BGN

2nd  SET

2nd  QUIT

2nd  FV

2nd   I/Y  1 2  ENTER

CE|C   CE|C   8.5   I/Y

36   N

1000  +|-   PMT

CPT   PV

I got PV=31,902

While the correct answer is 31, 894.

Feel free to point out my mistakes. Thank you very much.

Answer 1

your answer is partially right except a little trick

here the first payment is made immediately, that is at the beginning of the month rather than end of the month

therefore we will deduct present value of 1000 for first month as the payment is made immediately, assuming starting of the month

therefore deducting 1000* PVF (0.070833%,1) from 1000

1000 - (0.992.9665 *1000)

=$7.0335

thus 31902.52 - 7.0335 = 31895.4865

adjusting the decimals will get the value correct

as nothing is mentioned about decimals and answer is also not in decimals\

C/Y refers to compounding the amount at an interest rate however P/Y is calculating the present value only without compounding at a particular interest or discount rate