Annuities Calculator

Publish date: 2024-06-16

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For an Annuity Immediate:
Payment = 1
n = 5
Interest Rate = 10
Calculate Present Value, Accumulated Value

PV annuity immediate formula:

an\|i =	Payment * (1 - vn)
	i

Calculate v:

v =	1
	1 + i

v =	1
	1 + 0.1

v =	1
	1.1

v = 0.90909090909091

Calculate PV given i = 0.1, n = 5, and v = 0.90909090909091

a5\|0.1 =	1 * (1 - 0.909090909090915)
	0.1

a5\|0.1 =	1 * (1 - 0.62092132305916)
	0.1

a5\|0.1 =	1 * 0.37907867694084
	0.1

a5\|0.1 =	0.37907867694084
	0.1

a5|0.1 = 3.7908

AV annuity immediate formula:

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

Calculate AV given i = 0.1, n = 5

s5\|0.1 =	1 * ((1 + 0.1)5 - 1)
	0.1

s5\|0.1 =	1 * (1.15 - 1)
	0.1

s5\|0.1 =	1 * (1.61051 - 1)
	0.1

s5\|0.1 =	1 * 0.61051
	0.1

s5\|0.1 =	0.61051
	0.1

s5|0.1 = 6.1051

How much of AV is principal?:

Principal = Payment Amount * n
Principal = 1 * 5
Principal = 5

Calculate Interest Paid:

Interest Paid = Accumulated Value - Principal
Interest Paid = 6.1051 - 5

Interest Paid = 1.11

You have 1 free calculations remaining

What is the Answer?

Interest Paid = 1.11

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

Example calculations for the Annuities Calculator

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