Case Information:

Years until retirement: $30$

Amount to withdraw each year: $ $120,000$

Years to withdraw in retirement: $25$

Interest rate: $7\mathrm{.}5\%$

Inflation rate: $3\mathrm{.}0\%$

Real rate: $4\mathrm{.}37\%$

Employer's annual contribution: $ $1,500$

Years until trust fund distribution: $20$

Amount of trust fund distribution: $ $28,500$

In order to answer any of these questions, first we need to know how much your friend will need when she is ready to retire. Since this amount will be the same for each of the parts of the problem, solve for this amount below:

Amount needed at retirement: $1,803,638$ Need to account for inflation so use real rate

Taking first payment at end of first year of retirement

The amount your friend must save each year to fund her retirement is:

Verifying

Amount to save each year: $($$$30,227)$ $$1,803,637\mathrm{.}84$

The lump sum your friend must deposit today to fund her retirement is:

Lump sum deposited today: $($$$500,049)$ $$1,803,637\mathrm{.}84$

To find the amount of the annual deposit now, it is easier to break down the components of the problem. Doing so for each of the following to find your friend's annual deposit, we get:

Value of employer's contribution at retirement:

Value of trust fund at retirement:

Amount to save each year now:

Annual retirement payment in $31$ years equal to $$120,000$ in today's dollars

$ $(47,998)$ $$120,000\mathrm{.}00$

Growing annuity factor for retirement period $($wo r$-$g$)$ Need to account for $120$k payment increasing by $3\%$ each year for the duration of retirement

Dividing by r$-$g

Amount needed at retirement

PV now of amount needed at retirement

Growing annuity factor for working period $($wo r$-$g$)$

Dividing by r$-$g

Amount to save each year

Amount needed to save this year and then increasing by $3\mathrm{.}0\%$ each year to reach the amount needed at retirements