Question

1. Assume that you deposit $8,500 in each of years 1-16 in an account yielding .7% interest compounded annually. 23 years from today you withdraw $28,000 from the account. How much will be in your account 30 years from today?

2. Determine the semi-annual deposits required to accumulate $4,000 four years from today, given an annual interest rate of 12%, compounded semi-annually. (Assume your deposits begin 6 months from now and there are 8 total deposits)

Answer 1

1]   The first step is to find the FV of the annuity of $8500   
   for 16 years, EOY 16. It is:  
   = 8500*(1.07^16-1)/0.07 = $237,048.46
   FV of the above amount at EOY 30 = 237048.06*1.07^14 =   $611,236.52
   Less: FV of the amount withdrawn = 28000*1.07^7 = $44,961.88
   Amount in the account 30 years from today $566,274.64
2]   Amount to be deposited today = 4000/1.06^8 =   $2,509.65
   Note that the number of periods is 4*2 = 8 half years &  
   the interest rate per period is 12%/2 = 6%.