I need help with questions 6 through 9. O Lab Project Chapter 3 - Part B You hav
ID: 3113006 • Letter: I
Question
I need help with questions 6 through 9.
O Lab Project Chapter 3 - Part B 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. 1. How much will you need to put into this plan each month? _27s 39 2. How much total will you put into this plan? _ IISee3.8 3. How much interest did this plan earm while investing during the 35 years? 23433.2Explanation / Answer
1.The formula for the future value (F) of annuity is F = (P/r)[(1+r)n-1] where P is the periodic payment, r is the rate of interest, and n is the number of periods.
Here, F = $ 350000, r = 5.5 % /12 = 55/12000 = 11/2400, n = 35*12 = 420. We have to find P.
We have 350000= P[(1+11/2400)420-1]/(11/2400) so that P=(350000*11/2400)/[(1+11/2400)420-1] = (9625/6)/[(2411/2400)420-1] = 9625/[(6)*(6.825065742 -1)] = 9625/[(6)*(5.825065742)] = 9625/34.95039445 = $ 150.212897 = = $ 275.39 ( on rounding off to the nearest cent).
2. The amount paid is 420 *$275.39 = $ 115663.80
3. The interest earned by the plan in 35 years is $ 350000- $ 115663.80 = $ 234336.20
4. The annuity payment formula is P = r(PV)/[1-(1+r)-n] where PV is the present value, r is the rate of interest per period, n is the number of payments and P is the periodic payment. Here, PV is $ 350000 , r is 5.5 % /12 = 55/12000 = 11/2400, and n = 15*12 = 180so that P =(11/2400)*350000/[ (1-(1+11/2400)-180] = (9625/6)/(1-0.439061786]) = 9625/(6*0.560938214) = 9625/(3.365629284 = $ 2859.79( on rounding off to the nearest cent).
5.Since $ 2859.79*180 = $514762.20, the interest paid by the annuity during the 15 year repayment period is $514762.20-$350000 = $ 164762.20 ( the difference of 66 cents is due to rounding off).
6. The amount paid by the plan in retirement is $ 514762.20.
7. The amount earned from interest is $ 514762.20- $ 115663.80 = $ 399098.40.
8 The amount contributed to the retirement is (115663.80/514762.20)*100 % = 22.47 % ( on rounding off to the nearest hundredth)
9. We do not have sections 3.3 and 3.4 so it is not possible to offer exact comments. However, we have used only 2 formulae of which one is for determining the future value of an annuity and the second one is for determining a monthly annuity payment when a fixed sum of money is available. Withdrawing money from a retirement account works the same way as making a house payment because interest is computed on the reducing balance. Putting aside a small sum periodically, when one is young, makes a big difference at the time of retirement because of 2 factors, the first being the accumulation of periodic savings and the second is the interest earned on savings. The withdrawals from the retirement account are much more than the periodic savings because in case of savings, one starts with small amounts so that the interest earned during the initial period is also relatively small. However, at the time of withdrawal, a large sum is available initially itself which continues to earn substantial interest. The second factor is that the period of withdrawal is only 15 years so that the savings plus the interest thereon get distributed over a relatively smaller period ( the period over which savings accumulate is 35 years).