Question

our father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $60,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $130,000 saved, and he expects to earn 8% annually on his savings. How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round intermediate calculations. Round your answer to the nearest dollar.

$  

Answer 1

1. Real rate of return = [(1 + Nominal rate) / (1 + Inflation rate)] - 1

Real rate of return = [(1 + 0.08) / (1 + 0.03)] - 1

Real rate of return = 1.0485437 - 1

Real rate of return = 4.85437%

2. Present Value of receipts of $60000 for 25 years at age 60 = $899775.04

3. Future value of current savings after 10 years = savings * (1 + Interest)^Years

Future value of current savings after 10 years = 130000 * 1.0485437^10

Future value of current savings after 10 years = 130000 * 1.60644

Future value of current savings after 10 years = $208837.58

3. Amount required at the age of 60 years = $1209222.53 - 208837.58 = $928562.28

4. Annual savings required to reach the goal: $

Annual savings required to reach the goal: $64098