You want to be able to withdraw $35,000 from your account each year for 30 years

Question

You want to be able to withdraw $35,000 from your account each year for 30 years after you retire. If you expect to retire in 25 years and your account earns 5.2% interest while saving for retirement and 4.9% interest while retired:

Please show what formulas were used. I want to understand how to solve it.

https://mathas.pvc.maricopa.edu/assessment/showtest.php?actions skip&to;=20 MathAS Assessment Chapter 4 Handout C Search Q8A | Chegg.com Compound Interest Calcu. Aska homework question JIf you randomly selecta c W Poker probability Wikipe a Questions on Algebra Ave.. ue in ou ue Tue pm Show Intro/Instructions You've already done this problem. Score on last attempt: D 0 out of 5 (parts:0/1,0/1,0/1, 0/1,0/1) score in gradebook: 0 out of 5 (parts:0/1, 0/1,0/1,0/1,0/1) Try another similar question Question with last attempt is displayed for your review only Questions Q 2 [1.7/5] Q 3 [1.7/5] You want to be able to withdraw $35,000 from your account each year for 30 years after you retire. If you expect to retire in 25 years and your account earns 5.2% interest while saving for retirement and Round your answers to the nearest cent as needed 4.9% interest while retired Q 10 [5/5] Q 11 [5/5 a) How much will you need to have when you retire? S589342.84 Q 13 [5/5] b) How much will you need to deposit each month until retirement to achieve your retirement goals? C Q 15 (2.5/5) Q16 (0/5) C Q 17 (1.7/5) Q 18 [5/5] Q 19 [5/5] Q 20 (0/5) c) How much did you deposit into you retirement account? x Q 21 [0/5] d) How much did you receive in payments during retirement? Grade: 72.6/100 Print Version e) How much of the money you received was interest? Answer: 544223.7 Answer: 886.91 Answer: 266073 Answer: 1050000 Answer: 783927 6/28/2016

Explanation / Answer

a) The annuity payment formula used to calculate the periodic payment on an annuity is P = r(PV)/[ 1 – (1 +r)-n ] where PV is the present value, P is the periodic payment, r is the rate of interest for the period in decimals, and n is the number of periods. Here, P= $ 35000, n = 30 and r = 4 .9 % = 0.049. Then 35000 = 0.049 (PV) / [ 1 – ( 1+ 0.049)-30 ] = 0.049 (PV) /[ 1 – (1.049)-30 ] = 0.049 (PV) / [ 1 – 0.238086819 ] =0.049 (PV) / 0.76191318 so that PV = 35000*0.76191318/ 0.049 = 26666.9613/0.049 = $ 544223.70 ( on rounding off to the nearest cent).

b) The formula for computing the future value of annuity is F = P(1 + r)[ (1 + r)n -1] / r , where F is the future value, P is the is the periodic payment, r is the rate per period and n is the number of periods. Here, F = $ 544223.70, r = 5.2 %/ 12 = 0.052/12 =   0.00433333 and n = 25*12 = 300. Then 544223.70 = P ( 1 +   0.00433333 ) [ (1+ 0.00433333 )300 -1]/ 0.00433333 = P ( 1.0043333)[ 1.0043333)300 -1]/ 0.00433333 = P ( 1.0043333) [ 3.658969269 -1]/ 0.00433333   = (2.670491381)P/0.00433333 = 616.2719822 P. Hence, P =   544223.70/ 616.2719822 = $ 883.09( on rounding off to the nearest cent).

c) $ 883.09* 300 = $ 264927.04 was deposited into the retirement account.

d) An amount of $ 35000* 30 = $ 1050000 was received during retirement.

e) The amount of interest received was in 2 stages:

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