Answer:
Instructions are listed below.
Explanation:
Giving the following information:
Your 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 $55,000 has today.
Annual inflation is expected to be 3%. He currently has $135,000 saved, and he expects to earn 8% annually on his savings.
<u>We weren't provided with the requirements. Therefore I will answer in two different ways:</u>
a- to reach the goal the money will be deposit all in once.
b- to reach the goal the money will be deposit in annual payments.
First, we need to calculate the total money required at the age of 60.
FV= PV*(1+i)^n
i= 0.08 - 0.03= 0.05
n=10
PV= 135,000
FV= 135,000*(1.05^10)= 219,900.77
Total retirement needed= 55,000*24= 1,320,000
<u>Total money needed= 1,320,000 - 219,900.77= 1,100,099.23</u>
A) Lump sum:
PV= FV/ (1+i)^n
PV= 1,100,099.23/1.05^10= $675,365.50
B) Annual deposit:
FV= {A*[(1+i)^n-1]}/i
A= annual deposit
Isolating A:
A= (FV*i)/{[(1+i)^n]-1}
A= ( 1,100,099.23*0.05) / [(1.05^10) - 1]= 87,462.92
