Find the present value of an annuity with payments of $1,800 at the end of each year for 12 years. The interest rate is 8.5% compounded annually. Round to the nearest dollar.
Question
Find the present value of an annuity with payments of $1,800 at the end of each year for 12 years. The interest rate is 8.5% compounded annually. Round to the nearest dollar.
Solution
To find the present value of an annuity, we can use the formula for the present value of an ordinary annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
where:
- PV is the present value of the annuity,
- PMT is the amount of each annuity payment,
- r is the interest rate per period, and
- n is the number of periods.
In this case, PMT = $1,800, r = 8.5% or 0.085 (as a decimal), and n = 12 years.
Substituting these values into the formula, we get:
PV = 1800 * [(1 - (1 + 0.085)^-12) / 0.085]
Now, calculate the expression in the brackets:
= 1800 * [(1 - (1.085)^-12) / 0.085]
= 1800 * [(1 - 0.3976) / 0.085]
= 1800 * [0.6024 / 0.085]
= 1800 * 7.087
Finally, multiply the result by the annuity payment:
PV = 1800 * 7.087 = $12,757
So, the present value of the annuity is approximately $12,757 when rounded to the nearest dollar.
Similar Questions
Find the payment that should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment period.$118,000; monthly payments for 8 years; interest rate 9%.
Michelle purchases a retirement annuity that will pay her $2,500 at the end of every six months for the first nine years and $200 at the end of every month for the next three years. The annuity earns interest at a rate of 5.9% compounded quarterly. a. What was the purchase price of the annuity? Round to the nearest cent b. How much interest did Michelle receive from the annuity? Round to the nearest cent
Calculate the present value of an annuity due providing $200 every year for 4 years given the interest rate is 5%.Group of answer choicesNone of the options.$730.48$744.66$709.20
A company is considering the purchase of new equipment for $45,000. The projected annual net cash flows are $19,000. The machine has a useful life of 3 years and no salvage value. Management of the company requires a 12% return on investment. The present value of an annuity of $1 for various periods follows: Period Present value of an annuity of $1 at 12%1 0.89292 1.69013 2.4018 What is the net present value of this machine (rounded to the nearest whole dollar) assuming all cash flows occur at year-end?
A 20-year annuity of forty $5,000 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. a. If the discount rate is 11 percent compounded monthly, what is the value of this annuity 4 years from now?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.