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