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Ivanshal [37]
3 years ago
5

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per mont

h. You have access to an account that pays an APR of 7.2% compounded monthly. What size nest egg do you need to achieve the desired monthly yield?
What montly deposits are required to achieve the desired monthly yield at retirement?
Business
1 answer:
Triss [41]3 years ago
4 0

Answer:

623,459.79 and 224.51

Explanation:

first lets consider the first part of the problem and is how mucho do i need to accumulate for having an annuity for 25 years. this problem can be solved applying the concept of annuity, keep in mind that an annuity is a formula which allows you to calculate the present value of future payments affected by an interest rate.by definition the present value of an annuity is given by:

a_{n} =P*\frac{1-(1+i)^{-n} }{i}

where a_{n} is the present value of the annuity, i is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem, we have:

a_{25*12} =4,500*\frac{1-(1+0.006)^{-25*12} }{0.006}

look at the value 25*12 because the problem tells us is during 25 years but the payment is monthly, and look at the 0.006 and it is comming from the APR/12 and we must do that because this rate is componded Monthly:

a_{25*12} =623,459.79

so for the second part we must calculate the second part we must calculate the acumulated value at 40 years of work:

s_{n} =P*\frac{(1+i)^{n}-1 }{i}

where s_{n} is the future value of the annuity, i is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem, we have:

623,459.79 =P*\frac{(1+0.006)^{40*12}-1 }{0.006}

solving for P we have:

P=224.51

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