Assume you want to retire early at age $53.$ You plan to save using one of the following two strategies: $(1)$ save $$3,600$ a year in an IRA beginning when you are $28$ and ending when you are $53(25$ years$)$ or $(2)$ wait until you are $41$ to start saving and then save $$7,500$ per year for the next $12$ years. Assume you will earn the historic stock market average of $14\%$ per year. $($Click the icon to view the future value annuity factor table.$)($Click the icon to view the future value factor table.$)$

$($Click the icon to view the present value annuity factor table.$)$

Read the requirements.

$($Click the icon to view the present value factor table.$)$

Requirement $1.$ How much out$-$of$-$pocket cash will you invest under the two options?

Calculate how much out$-$of$-$pocket cash you will invest under the two options.

Option $1$:

Option $2$:

Requirement $2.$ How much savings will you have accumulated at age $53$ under the two options?

Calculate the total amount of savings that you will have accumulated at age $53$ under the two options. $($Round the savings to the nearest dollar amount.$)$ Option $1$: Option $2$:

Requirement $3.$ Explain the results.

The strategy involving

grows substantially larger over time. This is due to the fact that the savings are invested

so time does the work.

Requirement $4.$ If you were to let the savings continue to grow for nine more years $($with no further out$-$of$-$pocket investments$),$ under each scenario, what will the investment be worth when you are age $62?$ Calculate the total amount of savings at age $62,$ with no further out$-$of$-$pocket investments, under each scenario. $($Round the savings to the nearest dollar amount.$)$

Option $1$:

Option $2$: