Annuities Calculator

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For an Annuity Due:
Payment = 5000
n = 20
Interest Rate = 7
Calculate Present Value, Accumulated Value

PV annuity due formula:

än\|i =	Payment * (1 - vn)
	d

Calculate v:

v =	1
	1 + i

v =	1
	1 + 0.07

v =	1
	1.07

v = 0.93457943925234

Calculate d

d =	i
	1 + i

d =	0.07
	1 + 0.07

d =	0.07
	1.07

d = 0.065420560747664

Calculate PV given i = 0.07, n = 20, and d = 0.065420560747664

ä20\|0.07 =	5000 * (1 - 0.9345794392523420)
	0.065420560747664

ä20\|0.07 =	5000 * (1 - 0.25841900281387)
	0.065420560747664

ä20\|0.07 =	5000 * 0.74158099718613
	0.065420560747664

ä20\|0.07 =	3967.4583349458
	0.065420560747664

ä20|0.07 = 56677.9762

AV annuity due formula:

sn\|i =	Payment * ((1 + i)n - 1)
	d

Calculate AV given i = 0.07, n = 20, and d = 0.065420560747664

s20\|0.07 =	5000 * ((1 + 0.07)20 - 1)
	0.065420560747664

s20\|0.07 =	5000 * (1.0720 - 1)
	0.065420560747664

s20\|0.07 =	5000 * (3.8696844624862 - 1)
	0.065420560747664

s20\|0.07 =	5000 * 2.8696844624862
	0.065420560747664

s20\|0.07 =	14348.422312431
	0.065420560747664

s20|0.07 = 219325.8839

How much of the accumulated value is principal and interest?:

Principal = Payment Amount * n
Principal = 5000 * 20
Principal = 100000

Calculate Interest Paid:

Interest Paid = Accumulated Value - Principal
Interest Paid = 219325.8839 - 100000

Interest Paid = 119325.88

You have 1 free calculations remaining

What is the Answer?

Interest Paid = 119325.88

How does the Annuities Calculator work?

Free Annuities Calculator - Solves for Present Value, Accumulated Value (Future Value or Savings), Payment, or N of an Annuity Immediate or Annuity Due.
This calculator has 5 inputs.

What 4 formulas are used for the Annuities Calculator?

PV Annuity Immediate = Pmt * (1 - vn)/i
PV Annuity Immediate = Pmt * (1 - vn)/d
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/i
Accumulated Value of Annuity Immediate = Pmt * ((1 + i)n - 1)/d

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Annuities Calculator?

accumulated valueThe total value of an investment, including principal and interest accruedannuitiesannuityA stream of paymentsfuture valuethe value of a current asset at a future date based on an assumed rate of growthinterestpayment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rateinterest ratethe proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositorpresent valuethe value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.
PV = FV/(1 + i)n
where I is the interest rate per period, PV = Present Value, and FV = Future ValueprincipalThe amount borrowed on a loan, before interest is charged

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