# How to compare loan interest rate to savings account interest rate?

I don't understand how to compare my loan's interest rate to my savings account interest rate.

My savings account states:

The Interest Rate on your account is 4.0249% with an Annual Percentage Yield of 4.10%

Interest on your account will be compounded and credited on a monthly basis.

My loan states:

Interest Rate: 2.75%

Interest on your account is calculated using a simple daily interest formula. Simple interest is a formula that multiplies your loan balance by the number of days since the last payment, times the interest rate factor. Interest accrues daily on your loans.

Should I put excess income towards the loan or savings?

The question boils down to the taxes. If your loan is tax deductible (e.g.: mortgage loan or investment interest, and you're itemizing the deductions), then the tax benefit reduces the loan cost. Your interest income is likely taxable at marginal rates, which reduces the interest gain.

Let's assume your marginal Federal rate is 25% and State rate is 5% (check the actual numbers from your last year's tax returns). Total tax is 30%.

If your loan interest is deductible in full, the actual cost is 2.75%*0.7=1.925%. Your income, after taxes, is 4.10%*0.7=2.87%. In this scenario, clearly savings would yield a better result. Even if your loan is not deductible at all (a personal loan, or you are taking a standard deduction), 2.87% of your after-tax interest income is more than 2.75% of your loan cost.

With different tax rates, the calculations may yield different results. So, check the numbers for your personal situation.

• Of course, (relatively) few people people itemize tax deductions, especially if married filing jointly. also, 2.87% is so close to 2.75% (only \$12.50 in a \$10K savings account) that it makes no difference whether you put the money in savings or against the loan. Jul 6 at 13:53

Should I put excess income towards the loan or savings?

Depending on tax rates, and if are going to deduct the interest , you can calculate which is better mathematically.

But what is the savings for? Is it to use as an emergency fund to carry you through a job loss? is it to establish a "life happens" fund to cover an unexpected major car repair?

While paying extra principal on the loan, will save money, it generally comes by paying the loan off quicker and with less interest. Until the balance reaches zero you still have to make at a minimum the monthly payment as described in your loan paperwork. That means once put against the loan, there is no way to get it back if the car needs repairs in a few months.

The purpose of the savings may trump any mathematical calculation.

• Lucky for OP, he can have his cake and his liquidity too. (And with the money in the interest-bearing savings account, when the rates on that account change he can recalculate and make a new decision) Jun 22 at 15:04

Loan interest is front-loaded. Savings interest is compounded.

Use an amortization calculator/table and a savings calculator to visualize the interest and decide which one makes more sense.

\$100,000, 30-year @2.75% costs \$46,967 in interest.

Paying an extra \$200/month against the principal results in:

Loan paid off after 17 years, \$25,642 paid in interest.

Interest "saved" = \$21,325

Savings - Savings Calculator

Put away \$200/month for 17 years @4.10% into an account which started at \$4,000 results in \$21,555 interest earned.

Put away \$200/month for 17 years into an account which started at \$0 results in \$17,635 interest earned.

As always, what is your goal and what is your financial horizon? Can you actually do \$200/month for 17 years? Is your loan variable-rate? If so, then the math gets muddy. Will the APY be 4.10% indefinitely? Probably not. Are you better off risking your excess income on investments? Do you need an emergency fund?

There exist other considerations like taxes but I am not familiar with them so add these calculators to your financial arsenal.

• I always think of the same thing, but I never assume I can keep a payment and savings habit for more than a few years. Life changes quickly.
– user26460
Jun 22 at 14:22
• @user26460 Yep, "life" is always the trickiest variable when doing maths =) Jun 22 at 14:34
• "\$21,325 interest saved" but it's money that wouldn't have been due for another up-to 13 years, so it's PV (at year 17) is quite a bit less than that figure. You need one more scenario -- Put the money into savings until the compounded balance curve crosses the loan payoff curve (it'll happen before 17 years), and calculate "interest saved" for that scenario. Jun 22 at 15:02
• @MonkeyZeus: Not unexpected, because the savings rate is so much higher. But the additional scenario was to find when the savings account balance exceeds the remaining principle on the loan. Jun 22 at 15:27
• @thegreatemu I tend to interpret "excess income" as a continuous stream of excess monies. You should ask OP for clarification on whether they meant to describe a one-time windfall. There's plenty of "How should I prioritize my inheritance against my debts?" questions on this site which do align with your assumption of "I have \$X now." Jun 22 at 19:46

Perhaps I am overly simplifying things, but it seems to me the other answers are overly complicating this.

Every dollar in your bank account increases your net worth by one dollar, with 4.1% annual growth. Every dollar you owe on your loan decreases your net worth by one dollar, with 2.5% (negative) growth. Putting a dollar into excess loan payments is therefore equivalent to putting it into a savings account with 2.5% growth instead of 4.1%.

In other words, if you have a guaranteed way to get a higher return on some savings vehicle than your loan interest rate, that will increase your net worth fastest and is the better option from a strictly numerical point of view.

There are other concerns, but in this case they all favor putting excess money into savings:

• savings have higher liquidity
• deducting loan interest from taxes (in the unlikely case where you're not taking the standard deduction)
• Inflation decreases the real value of a loan over time (in a highly inflationary period, spending more of your excess money over early loan payoffs may actually be the best way to conserve wealth! Especially if spent on something with a real return like improving house insulation. )
• Inflation decreases the real value of the loan and savings the same amount. Jun 22 at 21:49