Question

Beginning 1 month from today David B. will deposit each month $200 into an account paying 6% nominal interest. He will make a total of 240 deposits (20 years). After the last deposit the money in the account will begin to earn 4% interest compounded annually. After another 10 years David will begin to withdraw annual amounts for a total of 10 years. How much can be withdrawn each year if the account is to be depleted (zero balance) after another 10 years?

Answer 1

The amount $16215.92 can be withdrawn each year.

Step-by-step explanation:

See the attached file for the calculations

Answer 2

$13,678.67

Step-by-step explanation:

This problem is better solved in phases as shown below:

First, we need to determine the future worth of the monthly deposit of $200 for 20 years.

=fv(rate,nper,pmt,-pv)

rate is the monthly rate of return which is 6%/12=0.5%

nper is the number of deposits to be made which is 240

pmt is the amount of each deposit which is $200

pv is the present worth of all whole deposits which is unknown and can be taken as zero.

=fv(0.5%,240,200,0)=$92,408.18

The $92,408.18 would now be invested for 10 years earnings 4% interest return annually,hence its future worth can be computed thus:

FV=PV*(1+r)^n

PV is the present value of $92,408.18

r is the 4% rate of return

n is the 10 years

FV=$92,408.18*(1+4%)^10=$136786.68

Now the amount that can be withdrawn for 10 years=136786.68/10= 13,678.67