High-yield savings calculator

What is a high-yield savings calculator?

A high-yield savings calculator estimates how large the balance in a high-yield savings account (HYSA) will grow over time. A HYSA is a deposit account that pays a much higher interest rate than a standard savings account, quoted as an annual percentage yield (APY). Because the APY already reflects compounding over a full year, the calculator can project your balance forward accurately from just four inputs: how much you start with, the APY, how much you add each month, and how many years you keep saving.

How does the calculator work?

You enter an initial deposit, the account’s APY, a fixed monthly contribution, and the time horizon in years. The calculator converts the yearly APY into an equivalent monthly rate, counts the number of months, grows the initial deposit, and grows each monthly contribution for the number of months it stays in the account. It then reports the final balance, the total you contributed, and the interest those deposits earned.

Because the APY is already an effective yearly figure, the tool derives a monthly rate from it rather than dividing by twelve. This keeps the projection consistent with the yield the bank advertises: leaving money in the account for a full year with no additions returns exactly the quoted APY.

Formula

The final balance combines the growth of the initial deposit with the growth of a stream of equal monthly contributions:

$FV = P \cdot (1 + i)^{n} + C \cdot \frac{(1 + i)^{n} - 1}{i}$

Where:

• $FV$ is the final balance.
• $P$ is the initial deposit.
• $C$ is the monthly contribution.
• $i$ is the effective monthly rate.
• $n$ is the total number of months.

The monthly rate and the month count come from the APY and the number of years:

$i = \left(1 + \frac{APY}{100}\right)^{1/12} - 1, \qquad n = 12 \cdot t$

where $APY$ is the annual percentage yield in percent and $t$ is the number of years.

Zero APY

When the APY is zero the contribution term would divide by zero, so it collapses to a plain sum of the deposits:

$FV = P + C \cdot n$

Examples of use

1. A starting deposit of 10,000 at a 4.5% APY, adding 200 every month for 5 years:

   • Initial deposit $P$ = 10000
   • Monthly contribution $C$ = 200
   • Monthly rate $i = (1.045)^{1/12} - 1 \approx 0.0036748$
   • Months $n$ = 60

   Calculation: $FV = 10000 \cdot (1 + i)^{60} + 200 \cdot \frac{(1 + i)^{60} - 1}{i} \approx 25860.17$

   The total contributed is 22,000 and the interest earned is about 3,860.17.

2. A one-off deposit of 5,000 at a 5% APY, with no monthly contributions, left for 10 years:

   • Initial deposit $P$ = 5000
   • Monthly contribution $C$ = 0
   • Months $n$ = 120

   Calculation: $FV = 5000 \cdot (1.05)^{10} \approx 8144.47$

   The total contributed is 5,000 and the interest earned is about 3,144.47.

Practical notes

• Compare accounts by APY, not by the nominal rate: the APY already folds in how often the bank compounds, so it is the fairest single number for ranking offers.
• HYSA rates are variable and track central-bank policy, so the APY you start with may not last the whole horizon; rerun the projection whenever your rate changes.
• Starting contributions early matters most, because each early deposit compounds for more months than a later one of the same size.
• A zero-APY run is a useful sanity check: the final balance should equal everything you put in, with no interest.

FAQs

What is the difference between APY and interest rate?

The interest rate is the nominal rate before compounding, while the APY is the effective yearly return after compounding is applied. Because this calculator works from the APY, it already accounts for compounding and needs no separate compounding-frequency setting.

Are high-yield savings account returns guaranteed?

The interest is credited as promised for as long as the advertised APY applies, but the rate itself is variable and the bank can change it. Unlike a certificate of deposit, a HYSA does not lock in a rate, so returns beyond the current period are estimates.

What happens if I only deposit once and never add more?

Set the monthly contribution to zero and the calculator projects the growth of the initial deposit alone, which is the classic compound growth of a single lump sum.