This gives a total of four different types of annuities and four different formulas to choose from: Formulas: Future Value of an Ordinary Annuity: FV = R[(1+i)^n - 1)/i] Future Value of an Annuity Due: FV = R[(1+i)^n - 1)/i(1+i)] Present Value of an Ordinary Annuity: PV = R[(1 - (1+i)^-n)/i] Present Value of an Annuity Due: PV = R[(1 - (1+i)^-n)/i(1+i)]
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First, understand the four types of annuities: a) Ordinary Annuity: Payments are made at the end of each period. b) Annuity Due: Payments are made at the beginning of each period. c) Future Value Annuity: The value of the annuity at a specific point in the Show more…
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Ordinary Simple Annuity Formula: Future Value of an Annuity FV = R [(1 + i)^n - 1] / i
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The future value of an ordinary annuity is given by the formula $F V=P M T\left[\left((1+i)^{n}-1\right) / i\right]$ where $P M T=$ amount paid into the account at the end of each period, $i=$ interest rate per period, and $n=$ number of compounding periods. If you invest 5,000 dollars at the end of each year for 5 years, you will have an accumulated value of $F V$ as given in the above formula at the end of the $n$ th year. Determine how much is in the account at the end of each year for the next 5 years if $i=0.06$.
Sequences and Series
We have used the formula A = R * [(1 + i)^n - 1] / i to find the future value of an ordinary annuity where payments are made at the end of each period. Another option allows the payments to be made at the beginning of each period. Such an annuity is called an annuity due. The future value of an annuity due at the end of n periods with periodic payments, R, at the beginning of each period is given by A = R * [(1 + i)^(n + 1) - (1 + i)] / i. Find the future value of an annuity due with monthly payments of $60 for 48 months. The annual interest rate is 3.6%. (Round your final answer to two decimal places.)
Adi S.
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