# Math

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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?

real interest rate = 6.94%
FV = 1.5 million
N = 40 yrs
pmt = \$7,630.72

Real amount each month is \$7,630.72

• Math - ,

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

• Math - ,

edfd

• Math - ,

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

• Finance - ,

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?