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# Annuities are explicated.

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Let's first define annuity. An annuity is a series of cashflow for a fixed number of periods. An ordinary annuity is when the payments (or cashflows) occur at the end of the period (for example, I pay you \$100/month for 12 month and the payment is made on the 31st of every month). An annuity due is when the payment is made on the first day of the period.

For ordinary annuities,

PV = (C/r)[1 - (1 + r)^(-n)], where r is interest rate, n is number of periods and C is per period payment.

FV = (C/r)[(1+r)^n - 1]

For annuity dues,

FV = (C/r)[(1 + r)^(n+1) - 1] - C.

Now we start answering the questions.

1.

a) This is an ordinary annuity. So FV = (C/r)[(1+r)^n - 1] = (3600/0.07)[(1+0.07)^12 - 1] = 64398.42.

b) This is an annuity due. FV = (C/r)[(1 + r)^(n+1) - 1] - C = (3600/0.07)[(1 + 0.07)^13 - 1] - 3600 = 68906.31.

There is no surprise that an annuity due is worth more than an ordinary annuity, because with annuity dues, you get the payments 1 period before the ordinary annuities, so you can start investin your payments earlier.

2. We assume that this is an ordinary annuity, when the payment time is not specified. This question is asking for the present value, there are ...

#### Solution Summary

Annuities are explicated.

\$2.19