Challenge question: You are planning to save for retirement over the next $40$ years. To do this, you

will invest $1,000$ a month in a share account and $1,000$ a month in a bond account. The return of

the share account is expected to be $6\%,$ and the bond account will pay $2\%.$ When you retire, you will

combine your money into an account with a $5\%$ annual return. How much can you withdraw each

month from your account, assuming a $25-$year withdrawal period?

Hint: To calculate your accumulated wealth $($FV$)$ in $40$ years you may find it easier to first calculate

the present value $($PV$)$ of your monthly investments $($using the annuity formula$)$ and then compound

the PV over $40$ years.