Explain the difference between an ordinary annuity and an annuity due. With an ordinary annuity, payments are made at the end of each period. With an annuity due, payments are made at the beginning of each period. Annuities due have lower interest rates than ordinary annuities. Annuities due have higher interest rates than ordinary annuities. Ordinary annuities earn simple interest. Annuities due earn compound interest. Ordinary annuities have fixed interest rates. With an annuity due, the interest rate may change.
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The following are the differences between annuity and compound interest EXCEPT: Annuity is an investment from which periodic withdrawals are made and compound interest earns interest on a growing basis since interest is earned on interest in addition to the original amount. Annuity requires a large sum of money as the initial investment and in compound interest, investing can be done even from a small fund. Annuity investment can be increased by investing in equity and bond sub-accounts and compound Interest investment value grows even in the absence of additional investment since interest earned increases automatically. The cash value of annuities can be figured using the compound interest table.
Jon S.
An annuity is a sum of money that is paid in regular equal payments. The _____ of an annuity is the sum of all the individual payments together with all the interest.
Sequences and Series
Mathematics of Finance
An annuity is a sequence of equal payments that are paid or received at regular time intervals. For example, you may want to deposit equal amounts at the end of each year into an interest-bearing account for the purpose of accumulating a lump sum at some future time. If, at the end of each year, interest of $i \times 100 \%$ on the account balance for that year is added to the account, then the account is said to pay $i \times 100 \%$ interest, compounded annually. It can be shown that if payments of $Q$ dollars are deposited at the end ofeach year into an account that pays $i \times 100 \%$ compounded annually, then at the time when the $n$ th payment and the accrued interest for the past year are deposited, the amount $S(n)$ in the account is given by the formula $$S(n)=\frac{Q}{i}\left[(1+i)^{n}-1\right]$$ Suppose that you can invest $\$ 5000$ in an interest-bearing account at the end of each year, and your objective is to have $\$ 250,000$ on the 25th payment. Approximately what annual compound interest rate must the account pay for you to achieve your goal? [Hint: Show that the interest rate $i$ satisfies the equation $50 i=(1+i)^{25}-1,$ and solve it using Newton's Method.]
THE DERIVATIVE IN GRAPHING AND APPLICATIONS
Newton’s Method
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