Question

1. Anna is planning to save $3 million for retirement over the next 30 years.

1. If she’s earning interest at a rate of 12% compound quarterly. How much money she should deposit each quarter.
2. If she lives after 25 years. What annual level of living expense will those saving support? (same interest rate of 12% compound quarterly.)
3. Suppose her retirement living expense will increase by $5000 each year. Determine the annual spending plan. (same interest rate of 12% compound quarterly.)

Answer 1

Assume end of period deposits and end of period withdrawals

a)

Rate of interest=i=12%/4=3%

Duration of deposit=n=30*4=120 quarters

Accumulated amount=FV=$3,000,000

Quarterly deposit=FV*(A/F,0.03,120)=3000000*(A/F,0.03,120)

Let us calculate the interest factor

Quarterly deposit=3000000*0.000889918=$2669.75

b)

Effective rate of interest=(1+3%)^4-1=12.550881%

Time period=n=25

Annual expense=3000000*(A/P,0.12550881,25)

Let us calculate the interest factor

Annual expense=3000000*0.132397846=$397,193.54

c)

Let the expense first year after retirement be R

So,

3000000=R*(P/A,0.12550881,25)+5000*(P/G,0.12550881,25)

Let us calculate the interest factors

(P/G,0.12550881,25)=49.814606465

3000000=R*7.552992974+5000*49.814606465

R=(3000000-5000*49.814606465)/7.552992974=$364216.80

Expense in first year $364,216.80 which increases by $5000 every year