Question

*Handwritten Answer preferred*

The Simpsons are planning to retire in 10 years. They currently have $200,000 in savings. In addition, they plan on adding to their savings by depositing $20,000 per year at the end of each year for the next 10 year.
a) [6 pts] Assuming they receive an interest of 7% compounded annually, how much will they have in their account at the end of 10 years?
b) [6 pts] At retirement, the Simpsons will deposit all of their savings (calculated in part a) in an account that will give them an interest rate of 10% compounded monthly. They would like to be able to withdraw money from this account for the next 20 years after retirement. How much can they withdraw each month in order to end up with a zero balance after the last withdrawal?

Answer 1

a

Future value = present value*(1+ rate)^time

Future value = 200000*(1+0.07)^10

Future value = 393430.27

FVOrdinary Annuity = C*(((1 + i )^n -1)/i)

C = Cash flow per period

i = interest rate

n = number of payments

FV= 20000*(((1+ 7/100)^10-1)/(7/100))

FV = 276328.96

Total FV = 393430.27+276328.96

=

669759.23

b

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

669759.23= Cash Flow*((1-(1+ 10/1200)^(-20*12))/(10/1200))

Cash Flow = 6463.32