John Smith wants $80,000 per year in his retirement. He plans to be in retirement for 30 years. He has 25 years to work. Assume an interest rate of 7% for the next 55 years. How much does he need to deposit at the end each year while he is working in order to have saved enough for retirement?

Its on Time of Vaule

To calculate how much John Smith needs to deposit at the end of each year while he is working in order to have enough saved for retirement, we can use the concept of present value.

The present value formula is given by:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value (the amount to be deposited each year)
PMT = Payment (the desired amount in retirement, which is $80,000 per year)
r = Interest rate (7%, expressed as a decimal, so 0.07)
n = Number of periods (in this case, the number of years in retirement, which is 30)

Now, let's put these values into the formula and calculate:

PV = $80,000 * [(1 - (1 + 0.07)^(-30)) / 0.07]

Calculating this equation will give us the amount that John Smith needs to deposit at the end of each year while he is working.