Question

A. You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $5000 per month. You have access to an account that pays an APR of 8.4% compounded monthly. This requires a nest egg of $626,174.58.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)

B. Suppose you want to save in order to purchase a new boat after retirement. Take the APR to be 6.0%. You want to have $17,000 toward the purchase of a boat in 3 years. How much do you need to deposit each month? (Round your answer to the nearest cent.)

Answer 1

Part (A)

Monthly deposits can be calculated using the PMT function of excel. Inputs are:

• Rate = APR of 8.4% compounded monthy = 8.4% / 12 = 0.7%
• Nper = number of months in 40 year = 12 x 40 = 480
• PV = 0
• FV = $ 626,174.58

Hence,  monthly deposits required to achieve the desired monthly yield at retirement = - PMT (Rate, Nper, PV, FV)

= - PMT (0.7%, 480, 0, 626174.58)

= $ 159.66

Part (B)

Monthly deposits can be calculated using the PMT function of excel. Inputs are:

• Rate = APR of 6% = 6% / 12 = 0.5%
• Nper = number of months in 3 year = 12 x 3 = 36
• PV = 0
• FV = $ 17,000

Hence,  monthly deposits required to achieve the desired monthly yield at retirement = - PMT (Rate, Nper, PV, FV)

= - PMT (0.5%, 36, 0, 17000)

= $ 432.17