aFinal answer:
To find the present value of an annuity, apply the formula involving payment amounts, the interest rate, and the number of periods. Multiply the payment by a factor derived from these variables. Round the final calculation to the nearest cent.
Step-by-step explanation:
The question concerns the calculation of the present value of an ordinary annuity. An annuity is a series of equal payments made at regular intervals, and the present value is the worth of these payments in today's dollars, given a specific interest rate. To find the present value of an ordinary annuity that involves payments of $1,600 per year for 19 years at a 9% annual interest rate, one would use the formula:
Present Value of Annuity = P × [((1 - (1 + r)^{-n}) / r)]
where P is the payment amount, r is the interest rate per period, and n is the total number of payments. Therefore:
Present Value of Annuity = $1,600 × ([(1 - (1 + 0.09)^{-19}) / 0.09])
Performing the calculation:
- Calculate (1 + r)^{-n}: (1 + 0.09)^{-19}.
- Subtract this value from 1.
- Divide the result by the interest rate (0.09).
- Multiply this by the payment amount ($1,600).
Once you have this final number, round to the nearest cent to find the present value of the annuity.