Question

You have $26290 to invest for retirement. You expect to retire in 22 years. A particular index fund has a long history of paying 8.53%, 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

Solution:-

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 = $26,290, r = 8.53%, n = 22 years

Fv = 26,290 * (1 + 8.53%) ^ 22

Fv = 26,290 * (1.0853) ^ 22

Fv = 26,290 * 6.0547

Fv = $159,179.176

So the investment of $26,290 will turn into $159,179.176 in 22 years at an interest rate of 8.53%.

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 = 8.53%

Inflation rate = 3.1%

1 + 8.53% = 1 + real rate * (1 + 3.1%)

1.0853 = 1 + real rate * 1.031

1.0853 / 1.031 = 1 + real rate

1.05267 = 1 + real rate

Real rate = 1.05267 - 1

Real rate = 0.0527 or 5.27%

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

Fv = PV * (1+r) ^ n

PV = $26,290, r = 5.27%, n = 22 years

Fv = 26,290 * (1 + 5.27%) ^ 22

Fv = 26,290* (1.0527) ^ 22

Fv = 26,290* 3.095

Fv = $81,367.55

So the real value is $81,367.55 at the time of retirement in 22 years.