You have decided that you will need $350,000 above what your current retirement
ID: 2492805 • Letter: Y
Question
You have decided that you will need $350,000 above what your current retirement plan contains to survive and have a little fun when you retire. At the age of 30, you decide to start putting an amount into an annuity once a month. The account earns 5.5% compounded monthly. You plan to retire at the age of 65. Your savings plan is for exactly 35 years. Show your work and the formula used.
The purpose of this project is to broaden your awareness of how saving just a small amount per month over the years working in a career combined with the interest your investment will earn becomes a substantial savings for your retirement. In recapping what you have just calculated, please answer the following questions.
Remind yourself of how little you contributed per month_______________________
Remind yourself of how much you actually invested in the plan__________________
What was the total dollars the plan paid you in retirement? _____________________________________________________________
How much of this was earned from interest (remember this amount will include the interest earned while investing in the plan and while receiving money from the plan)? ______________________________________________________________
So basically the amount you contributed to your retirement was approximately what percentage of the total amount received? 8. 10% , 25%, 50%, 75% This is math 1324. Also, I need these worked out please!
Explanation / Answer
FV of Ordinary Annuity = R * [(1+i)^n -1] / i
i is the interest rate per compounding period;
n are the number of compounding periods; and
R is the fixed periodic payment.
we have to find the monthly payment to make $350000 after 35 years at 5.5% compounded monthly.
Reorganising the above formula we get,
R = FV * i / [(1+i)^n - 1]
where n = 35 *12 = 420 months
r = 5.5%/12 per month
FV = $350000
applying the bove formula we get,
R = 350000*(5.5%/12) / ((1+(5.5%/12))^420-1) = $275.39
Remind yourself of how little you contributed per month
Answer: $275.39 per month
Remind yourself of how much you actually invested in the plan
Answer: Investment = $275.39 * 420 = $115663.80
What was the total dollars the plan paid you in retirement?
Answer: $350000
How much of this was earned from interest (remember this amount will include the interest earned while investing in the plan and while receiving money from the plan)?
Answer: $350000 - $115663.80 = $234336.20
The percentage of contribution to the total amount received under the plan = $115663.80 / $350000 = 33% (rounded to zero decimal place)
FV of Ordinary Annuity = R * [(1+i)^n -1] / i
i is the interest rate per compounding period;
n are the number of compounding periods; and
R is the fixed periodic payment.
we have to find the monthly payment to make $350000 after 35 years at 5.5% compounded monthly.
Reorganising the above formula we get,
R = FV * i / [(1+i)^n - 1]
where n = 35 *12 = 420 months
r = 5.5%/12 per month
FV = $350000
applying the bove formula we get,
R = 350000*(5.5%/12) / ((1+(5.5%/12))^420-1) = $275.39
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