Question

You have $23350 to invest for retirement. You expect to retire in 50 years. A particular index fund has a long history of paying 8.35%, and inflation is estimated to be 3.1%.
a) If you invest in that fund what would you expect your actual saving to be when you retire? $  
b) What will your real value be at the time you retire?

Answer 1

ANSWER:

A) In order to find the actual saving we will have to find the future value of this investment.

fv = pv * (1+r) ^ n

pv = $23,350 , r = 8.35% , n = 50 years

fv = 23,350 * ( 1 + 8.35%) ^ 50

fv = 23,350 * (1.0835) ^ 50

fv = 23,350 * 55.1373

fv = $1,287,456.81

so the investment of $23,350 will turn into $1,287,456.81 in 50 years at an interest rate of 8.35%

b) In order to find the real value , we will have to find the real rate of return which will be determined by fisher's equation.

1+ nominal rate = 1 + real rate * ( 1 + inflation rate)

nominal rate = 8.35%

inflation rate = 3.1%

1 + 8.35% = 1 + real rate * ( 1 + 3.1%)

1.0835 = 1 + real rate * 1.031

1.0835 / 1.031 = 1 + real rate

1.0509 = 1 + real rate

real rate = 1.0509 - 1

real rate = 0.0509 or 5.09%

In order to find the real value we will have to find the future value of this investment.

fv = pv * (1+r) ^ n

pv = $23,350 , r = 5.09% , n = 50 years

fv = 23,350 * ( 1 + 5.09%) ^ 50

fv = 23,350 * (1.0509) ^ 50

fv = 23,350 * 11.9815

fv = $279,768.88

so the real value is $279,768.88 at the time of retirement in 50 years.