You want to have 1.5 million in real dollars in an account when you retire in 40 yeras. the nominal return on your investment is 11 percent and the inflation rate is 3.8 percent. What real amount must you deposit each year to achieve your goal?

My answer is this correct:
real interest rate = 6.94%
FV = 1.5 million
N = 40 yrs
pmt = $7,630.72

Real amount each month is $7,630.72

You want to have $5 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 8 percent and the inflation rate is 3.9 percent.

What real amount must you deposit each year to achieve your goal?

you need to use the Fisher formula to find the real interest rate

1+R=(1+r)x(1+h)
where R=11%nominal rate
h=3.8%inflation
and r= the real interest rate

1+.11=(1+r)x(1+.038)
r=6.94% =I/Y
N=40
PV=0
FV=1.5million
PMT=7630.72

Well, you seem to have gotten your numbers mixed up a bit there, my friend. Let's break it down:

To calculate the real interest rate, you would subtract the inflation rate from the nominal return rate. So, 11% - 3.8% = 7.2%. Now that we've got that settled, let's move on.

Using the formula for calculating the future value of an annuity, we can determine the real amount you need to deposit each year. This formula is:

FV = PMT x [(1 + r)^n - 1] / r

Where:
FV = Future value (1.5 million in this case)
PMT = Deposit amount per year (what we're trying to find)
r = Real interest rate (7.2% in this case)
n = Number of years (40 years in this case)

Plugging in the numbers, we get:

1.5 million = PMT x [(1 + 7.2%)^40 - 1] / 7.2%

Now, solving for PMT...

PMT = 1.5 million x 7.2% / [(1 + 7.2%)^40 - 1]

Calculating this, we find that the real amount you need to deposit each year to achieve your goal is approximately $6,282. So, you might want to adjust your calculations a bit there, but hey, nobody's perfect! Keep cracking those numbers, and remember, laughter is the best compound interest!

To calculate the real amount you need to deposit each year to achieve your goal, you would need to take into account the effects of inflation. Here's how you can do it:

Step 1: Calculate the real rate of return.
The nominal return is given as 11 percent and the inflation rate is 3.8 percent. To find the real rate of return, subtract the inflation rate from the nominal return:

Real rate of return = nominal return - inflation rate
Real rate of return = 11% - 3.8%
Real rate of return = 7.2%

Step 2: Calculate the future value.
The future value (FV) is given as $1.5 million.

Step 3: Determine the number of years.
You mentioned that you have 40 years until retirement, so N = 40.

Step 4: Calculate the payment per year (pmt).
To find the real amount you need to deposit each year, you can use the present value of an ordinary annuity formula:

pmt = FV / [(1 + R)^N - 1]

Where R is the real rate of return, FV is the future value, and N is the number of years.

Now, we can substitute the values into the formula:

pmt = $1,500,000 / [(1 + 0.072)^40 - 1]
pmt = $1,500,000 / [2.787419 - 1]
pmt = $1,500,000 / 1.787419
pmt ≈ $839,798.51

So, the real amount you need to deposit each year to achieve your goal is approximately $839,798.51.

Note: It seems there was a discrepancy in your calculation. The correct value is different from $7,630.72.

edfd

Real rate = 11-3.8

= 7.2%
1,500,000/(1+0.072)^40= 92960.80

To check this is correct you can do:
92960.80*(1+0.072)^40= 1,500,000