You plan to retire in 30 years and plan on saving $15,000 annually, starting next year, for the next 30 years. You expect to need $120,000 about 18 years from now for college tuition for your recently born daughter which must be paid out of these savings. You expect to live 35 years during retirement (the first retirement payment will be 31 years from today).

a. If you assume an interest rate of 8.15% over the entire period, how much will you have available to spend annually in retirement in assuming you plan to purchase a $200,000 summer retirement home five years after you retire (the purchase will be made in year 35)?

b. Same as part a, except that interest rate is 5%. Does your retirement quality of live improve significantly? Assume the same college tuition and retirement home price.

c. If interest rate is 5%, but you want to keep the same retirement quality of life as if the interest rate is 8.15%. How much extra money do you need to save annually?

Please show detailed solutions and I will offer max points!!! Thank You!