Question

You want to have $2 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 12 percent and the inflation rate is 3.6 percent.

  

What real amount must you deposit each year to achieve your goal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Assume that the r is real rate of interest

Nominal rate = Real rate * Inflation rate

(1+ 12%) = (1 + r) * (1+ 3.6%)

Or 1.12/ 1.036 = (1 + r)

Or r = 1.08108 -1 = 0.08108 or 8.108%

Now we can use FV of an Annuity formula to calculate the annual deposits by you

FV = PMT *{(1+r) ^n−1} / r

Where,

Future value of annual deposits FV = $2,000,000

PMT = Annual deposits =?

n = N = number of payments = 30 years

r = I/Y = real interest rate per year = 8.108%

Therefore,

$2,000,000 = Annual deposit *{(1+ 8.108%) ^30−1} /8.108%

Annual deposits = $17,307.88

Therefore you have to deposit $17,307.88 per year to achieve your goal.