Most Americans want -- and need -- more than a million dollars in savings to retire without financial worries. Having a seven-figure nest egg should allow most families to replace the income they made while working, although seniors who have substantial healthcare needs may require even more money to fully cover the costs of their prescriptions and other care expenditures. 

401K in gold letters

Image Source: Getty Images.

Saving this much money may sound out of reach, and for families living paycheck-to-paycheck, it's definitely hard to find the cash to put toward retirement. But if you're committed to becoming a financially secure senior and willing to make some sacrifices, you can take advantage of accounts created to make saving easier by providing you with generous tax breaks. In fact, there are three key retirement accounts you can use to amass a substantial nest egg with a little help from the government. 

1. Your 401(k) plan

Around three-fourths of employers in the U.S. offered access to a 401(k) plan to workers in 2016, while those who are self-employed can open a one-participant 401(k) as long as they have no employees other than their spouse.  If you have access to a 401(k) at work, or can open one yourself, you can contribute up to $18,000 tax-free in 2017. If you're 50 or older, catch-up contributions allow you to bump this contribution to $24,000.

Because a 401(k) allows you to invest with pre-tax funds, your $18,000 contribution will net you a $4,500 discount on your taxes if you are in the 25% tax bracket, so your contribution would only reduce your take-home pay by $13,500. Many employers match a percentage of contributions, so if you were earning $60,000 and your employer matched 6% of your salary, your employer would provide another $3,600 in essentially free money. You'd take home $13,500 less but would put $21,600 into retirement savings. 

How much would this turn into by the time you retire? It depends upon your age when you begin maxing out your 401(k). If you max out your 401(k) from age 30 to your retirement at 65, your account would be worth more than $3 million by the time you retire if you earn a 7% return -- you'd be rich! If you wait until age 45 to begin maxing our your accounts, you'd still end up with close to $1 million by 65. 

2. An IRA account 

An IRA also gives you tax breaks for saving for your future, and you don't need an employer to create one. Depending upon your income, you can contribute up to $5,500 with pre-tax funds if you're under 50, and up to $6,500 if you're over 50, as of 2017.

If you're in the 25% tax bracket, you'd save $1,375 on your taxes by maxing out your IRA, so your contribution would cost you just $4,125. Those $5,500 annual contributions would turn into $739,567 if you invested from age 30 to 65 and made a 7% return.  If you get a later start and begin at 45, you'd still acquire just over $219,000 -- which would put you over the top of that $1 million mark when combined with maxing out a 401(k). 

3. A health savings account

Health savings accounts allow you to invest with pre-tax funds, provided you have a "high-deductible" health plan. As of 2017, this means your plan must have an individual deductible of at least $1,300 or a family deductible of $3,600. You're allowed to invest as much as $3,400 per person and $6,750 per family as of 2017, with people 55 and up entitled to an additional $1,000 catch-up contribution.  If you're in the 25% tax bracket and you max out your $3,400 contribution, you'll get an $850 tax break and reduce your take-home pay by $2,550 to make your maximum contribution. 

Maxing out this account by making $3,400 contributions from age 35 to age 65 would net you $343,648 in savings by the time you retire, if you do not take money out to pay for medical expenses during the years you were investing.  This would be enough to cover the $350,000 in healthcare costs the Employee Benefit Research Institute recommends senior couples save to be prepared for high healthcare and prescription drug costs. Even if you begin saving later, at age 45, you'll have around $149,141.  If you and your spouse both contribute and you maxed out your family account beginning at age 45, you'll still have about $300,000 to cover you as a couple, despite not investing until later in life. The money from HSAs can be withdrawn tax free to pay for out-of-pocket healthcare expenditures. 

While it may seem like a lot to invest in all three of these tax-advantaged accounts, the tax deductible contributions give you the chance to have the government subsidize your savings. Plus, as you can see, maxing out all these accounts would mean you'd save a fortune. Even if you can't quite max them all out, contributing cash to each could still leave you in very good shape when retirement arrives. 

The Motley Fool has a disclosure policy.