Question

You want to have $3 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10 percent and the inflation rate is 4.8 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.)Deposit amount $

Answer 1

Answer: $25078

Step-by-step explanation:

Firstly, we'll find the real interest rate which will be:

(1 + R) = (1 + r)(1 + h)

(1 + 10%) = (1 + r)(1 + 4.8%)

(1 + 0.1) = (1 + r)(1 + 0.048)

1.1 = (1 + r)(1.048)

r = 4.96%.

Now the annual deposit will be gotten by using the annuity future value which will be:

3 million = C(1.0496^40-1) / 0.0496

3 million = C(5.3995) / 0.0496

3 million = 119.627C

C = 3 million/119.627

C = 25078

Therefore, the real amount that must be deposited each year to achieve the goal is $25078