Calculate how much to save each month to reach a savings goal by a date, or how long a monthly deposit takes to get there, with interest.
Diperbarui Contoh terverifikasi: 6
Put aside $662.08 a month for 5 years to reach $50,000.00: $5,000.00 you already have, $39,724.61 of new deposits and $5,275.39 of interest.
| Tahun | Deposits | Bunga | Sisa saldo |
|---|---|---|---|
| 1 | $7,944.92 | $351.00 | $13,295.92 |
| 2 | $7,944.92 | $688.98 | $21,929.82 |
| 3 | $7,944.92 | $1,040.74 | $30,915.49 |
| 4 | $7,944.92 | $1,406.83 | $40,267.24 |
| 5 | $7,944.92 | $1,787.84 | $50,000.00 |
The denominator is the value of 60 deposits of 1.
The monthly deposit needed is what closes the gap between the goal and what your current savings will grow to: C = (G − S(1 + i)^n) ÷ (((1 + i)^n − 1) ÷ i), where G is the goal, S the amount already saved, i the monthly rate and n the number of months. In the other mode, the number of months comes from logarithms of the same equation and is rounded up to the month in which the goal is reached.
With the defaults, reaching 50,000 in 5 years from 5,000 already saved at 4% a year takes 662.08 a month. The 60 deposits add up to 39,724.61, and interest supplies the remaining 5,275.39 on top of the 5,000 you started with.
Interest is compounded monthly at a fixed rate, with deposits at the end of each month unless you choose the start under More options. Tax on interest and changes in the rate are not included.
Sumber pemeriksaan: Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000)
Sumber pemeriksaan: Python decimal, annuity-due factor: 659.8772…
Sumber pemeriksaan: 12000 / 12 by definition
Sumber pemeriksaan: Starting balance exceeds the goal, so no deposit is needed
Subtract what your current savings will grow to from the goal, then divide by the annuity factor ((1 + i)^n − 1) ÷ i. To reach 50,000 in 5 years from 5,000 at 4% compounded monthly, you need 662.08 a month; Excel's =PMT(4%/12, 60, -5000, 50000) gives the same. With no interest the same goal takes (50,000 − 5,000) ÷ 60 = 750 a month.
Solve the savings equation for the number of months and round up. Starting from 5,000 and saving 500 a month at 4%, the balance first passes 50,000 in month 77, after 6 years 5 months; raising the deposit to 750 cuts that to 54 months. Excel's NPER function solves the same equation.
More the longer the horizon. Over 5 years, 4% interest cuts the deposit needed for 50,000 from 750 to 662.08 a month, and 5% cuts it to 640.87. Over 10 years at 4%, the deposit falls to 288.94 a month and interest supplies 10,327.63 of the 50,000.
Slightly: a deposit made at the start of the month earns one extra month of interest. For 50,000 in 5 years from 5,000 at 4%, the deposit needed is 659.88 at the start of each month against 662.08 at the end, a difference of 2.20 a month.
Akurasi bergantung pada masukan dan asumsi metode. Aritmetika desimal memakai 50 digit signifikan, tetapi perkiraan, metode numerik dan data sumber bisa kurang presisi; pembulatan yang ditampilkan tidak menghilangkan batasan itu. Contoh penyelesaian yang diperiksa dengan sumber independen: 6. Misalnya, “50,000 in 5 years from 5,000 at 4%” diperiksa dengan Python decimal: (50000 − 5000·(1+0.04/12)^60) / (((1+i)^60 − 1)/i) = 662.0768…; same as Excel =PMT(4%/12,60,-5000,50000).
Microsoft Excel PMT function; Microsoft Excel NPER function.
Hanya untuk perencanaan. Pemberi pinjaman, otoritas pajak dan pasar menerapkan pembulatan, biaya dan aturan sendiri; konfirmasikan angka kepada mereka sebelum membuat komitmen.
Kalkulator ini mencakup 6 contoh perhitungan dengan jawaban dari sumber independen. Contoh tersebut dijalankan dalam rangkaian pengujian dan dapat Anda jalankan di sini juga.
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