Calculating Annuity Values - Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with a retirement income of $25,000 per month for 20 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $340,000. Third, after he passes on at the end of the 20 years of withdrawals, he would like to leave an inheritance of $1,000,000 to his nephew Frodo. He can afford to save $2,200 per month for the next 10 years. If he can earn an EAR of 11 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30?

Required:

a. Calculate the effective monthly rate of 11% and 7% (these are effective annual rates given). (Hint: use the nominal formula, or find the APR based on monthly compounding and divided by 12).

b. Calculate the present value of the $25,000 payments for 240 months at the EAR of 7%.

c. Calculate the present value of the $1,000,000 payments for 20 years at the APR of 7%.

The sum of the answer to part b and c gives us the amount that he needs at retirement.

d. Calculate the future value of the $2,200 monthly payments for 120 months at the EAR of 11%

e. Calculate the amount remaining after the purchase of the cabin (in 10 years)

f. Calculate the future value of the remainder (answer to part e) at the EAR of 11% for 240 months

The answer to part f is the amount of savings he will have before retirement.

g. Calculate the shortfall of the amount required at retirement and its future value

h. Calculate the Monthly payment needed from the purchase of the cabin to the start of retirement at the EPR of 11% for 240 months