How would you approach this using the excel functions of pv and pmt?
Here's the question:
You want to accumulate $1 million by your retirement date, which is 25 years from now. you will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises at 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e, your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc.) How much must your first deposit be if you are to meet your goal.

To approach this using Excel functions, we can use the PV (present value) and PMT (payment) functions to calculate the amount of the first deposit. Here are the steps:

1. Calculate the future value of the $1 million using the FV (future value) function:

=FV(8%, 25, 0, -1000000)

This returns a value of $4,660,962.91, which is the amount that will accumulate in 25 years at 8% interest.

2. Calculate the present value of the future amount using the PV function:

=PV(8%-3%, 25, -1*FV(8%, 25, 0, -1000000), 0, 1)

This returns a value of $1,257,407.11, which is the amount that needs to be deposited today to accumulate to $4,660,962.91 in 25 years at 8% interest with 3% annual raises.

3. Calculate the payment amount using the PMT function:

=PMT(8%, 25, -1*PV(8%-3%, 25, 0, 1257407.11, 1), 0, 1)*(1+3%)

This returns a value of $68,527.78, which is the amount of the first deposit.

So, the first deposit should be $68,527.78 to accumulate $1 million in 25 years with 8% interest, 3% annual raises, and 3% increase in deposit each year.