Question

After graduating from college with a bachelor of business administration, you begin an ambitious plan to retire in 25.00 years. To build up your retirement fund, you will make quarterly payments into a mutual fund that on average will pay 10.12% APR compounded quarterly. To get you started, a relative gives you a graduation gift of $3,814.00. Once retired, you plan on moving your investment to a money market fund that will pay 6.96% APR with monthly compounding. As a young retiree, you believe you will live for 29.00 more years and will make monthly withdrawals of $10,129.00. (YOUR WITHDRAWALS ARE AT THE BEGINNING OF THE MONTH!!!!) To meet your retirement needs, what quarterly payment should you make? Answer Format: Currency: Round to: 2 decimal places. Enter Answer Here...

Answer 1

First , we need to find the amount in the retirement fund

which is the Present Value of the beginning-of the- month withdrawals during retirement

so, using the PV of (beginning -of -the- mth)annuity due formula,

PV=(Pmt.*(1-(1+r)^-n)/r)*(1+r)

where, PV = the amt. in the retirement fund

Pmt.= the beginninf-of-the mth. Withdrawals--ie. $ 10129

r= the monthly int.ie. 6.96% APR compounded monthly

so, monthly r=(1+0.0696)^(1/12)-1, ie. 0.5623% 0r 0.005623 p.m.

n= no.of mthly. Withdrawals, ie. 29 yrs. *12 mths.= 348

Now, plugging in the values, in the above formula,

PV=(10129*(1-(1+0.005623)^-348)/0.005623)*(1+0.005623)

1554094.61

So, now, future value of the quarterly savings PLUS the FV of the single sum ,namely, the relative' s gift --must equal the above fund amt. ie. 1554094.61

so, using the FV of ordinary, end of the quarter --annuity + FV of the gift(single sum at time 0)=The Fund amt.

Retirement fund=(Pmt.*((1+r)^n-1)/r)+(Gift*(1+r)^n)

where,

the retirement fund to be accumulated= $ 1554094.61

Pmt.= The quarterly pmt. To build up the fund--- to be found out--??

r= the quarterly rate, ie. 10.12% APR compounded quarterly

so, quarterly r=(1+0.1012)^(1/4)-1, ie. 2.44% 0r 0.0244 per quarter

n= no.of quarters till buiding up the fund, ie. 25 yrs.*4= 100 Quarters

Gift amt.=Relatives gift----$ 3814

Now, plugging in the values, in the above formula,

1554094.61=(Pmt.*((1+0.0244)^100-1)/0.0244)+(3814*(1+0.0244)^100)

Solving the above, we get the quarterly payment to be made for 25 yrs. , as

3636.72

(ANSWER)