Amortization calculator

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An amortization calculator is used to determine the amount of periodic payments due on a loan (usually a mortgage), based on the amortization process.

The amortization payment model pays the various interest and principal amounts to each installment, even though the total amount of each payment is the same.

An amortization schedule calculator is often used to adjust the loan amount until monthly payments will fit within the budget, and can vary the interest rate to see better level differences that may be made in the type of house or car that can be bought. The amortization calculator may also disclose the exact dollar amounts intended for interest and the exact amount of money that goes into the principal of each individual payment. The amortization schedule is a table that describes these figures along the loan duration in chronological order.

Video Amortization calculator

Rumus

The calculations used to arrive at the amount of periodic payments assume that the first payment is not due on the first day of the loan, but rather a full repayment period into the loan.

Although it is usually used to solve A, (payment, by condition) can be used to resolve any single variable in the equation as long as all other variables are known. One can reset the formula to complete for one term, except for i , which can use the root search algorithm.

The annuity formula is:

${\ displaystyle A = P {\ frac {i (1 i) ^ {n}} {(1 i) ^ {n} -1}} = {\ frac {P \ times i} {1- (1 i) ^ {- n}}} = P \ left (i {\ frac {i} {(1 i) ^ {n} -1}} \ right )}  ÂÂ$

Where:

• A = amount of the regular payment
• P = principal amount, after the initial payment, which means "subtract payment below"
• i = periodic interest
• n = total payment amount

Rumus ini valid jika i & gt; 0. Jika i = 0 maka cukup A = P / n .

Untuk pinjaman 30 tahun dengan pembayaran bulanan, ${\ displaystyle n = 30 {\ text {years}} \ times 12 {\ text {months/year}} = 360 {\ text {months}}}  ÂÂ$

Note that the interest rate is usually referred to as the annual percentage rate (eg 8% APR), but in the above formula, due to monthly payments, the ${\ displaystyle i}$ should be in percent percent monthly. Changing the annual interest rate (that is, percent of annual results or APY) to the monthly rate is not as simple as dividing by 12; see the formulas and discussions in APR. However, if the tariff is expressed in "APR" instead of "annual interest rate", then dividing by 12 is the right way to determine the monthly interest rate.

Maps Amortization calculator

The derivation of the formula

Ini mungkin disamaratakan

${\ displaystyle \; p (t) = Pr ^ {t} -A \ jumlah _ {k = 0} ^ {t-1} r ^ {k}}  ÂÂ$

Menerapkan substitusi (lihat progresi geometrik)

${\ displaystyle \; \ sum _ {k = 0} ^ {t-1} r ^ {k} = 1 r r ^ {2} ... r ^ {t-1} = {\ frac {r ^ {t} -1} {r-1}}}  ÂÂ$

Ini menghasilkan

${\ displaystyle \; p (t) = Pr ^ {t} -A {\ frac {r ^ {t} -1} {r-1}}}  ÂÂ$

Untuk ${\ displaystyle n}  ÂÂ$ periode pembayaran, kami berharap jumlah pokok akan benar-benar lunas pada periode pembayaran terakhir, atau

${\ displaystyle \; p (n) = Pr ^ {n} -A {\ frac {r ^ {n} -1} {r-1}} = 0}  ÂÂ$

Memecahkan untuk A, kita dapatkan

${\ displaystyle \; A = P {\ frac {r ^ {n} (r-1)} {r ^ {n} -1}} = P {\ frac {(i 1) ^ {n} ((i {\ cancel {1}}) - {\ cancel {1}})} {(i 1) ^ {n} -1}} = P {\ frac {i (1 i) ^ {n}} {(1 i) ^ {n} -1}}}  ÂÂ$

atau

${\ displaystyle {\ frac {A} {P}} = {\ frac {i} {1- (1 i) ^ {- n}}}}  ÂÂ$

Setelah substitusi dan penyederhanaan yang kita dapatkan

${\ displaystyle {\ frac {p (t)} {P}} = 1 - {\ frac {(1 i) ^ {t} -1} {(1 i) ^ {n} -1}}}  ÂÂ$

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Penggunaan lainnya

Although often used for mortgage-related purposes, the amortization calculator can also be used to analyze other debts, including short-term loans, student loans, and credit cards.

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See also

• Amortization of loan

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External links

• Amortize the calculator in Curlie (based on DMOZ)

Source of the article : Wikipedia