Question

a) You have $216,000 in an account earning 1.5% per year. You plan to make 15 annual withdrawals out of this account starting 4 years from today. What are the equal annual withdrawals you can make that will deplete the account at the end?

b) You'd like to buy a 40-foot used catamaran in 12 years for $454,000. You already have $56,000 saved in an account earning a monthly interest rate of 0.31%. Your plan is to make monthly deposits into this account in order to save enough to buy the catamaran. How much would you need to save monthly?

Answer 1

a) PV = 216,000

r = 1.5%

First let's find the future value at year 4

FV4 = PV * (1 + r)^n

n = 4

FV4 = 216,000 * (1 + 0.015)^15

FV4 = 216,000 * 1.2502320667

FV4 = $270,050.1264072

Now, we will find the annual withdrawals for 15 years with this as PV

n = 15

Annual withdrawals = $19,939.6381477698

b) Future value of our savings:

FV12 = PV * (1 + r)^n

n = 12 * 12 = 144 months

FV12 = 56,000 * (1 + 0.0031)^144

FV12 = 56,000 * 1.5615977669

FV12 = 87,449.4749464

We still need to have (454,000 - 87,449.4749464) = $366,550.5250536

We will find the monthly deposit required to have FV = $366,550.5250536 in 144 months

Monthly payment required = $2,023.3460576932