Question

How much must be deposited in an account to have annual withdrawals of $1000 forever? Interest is compounded quarterly and the interest rate is 9% for the first 10 years and 10% thereafter.

Answer 1

In the given problem, the rate of interest is compounded quarterly and the interest rate is 9% so the effective rate of interest will be as

where i = rate of interest

m=the quarterly compounding factor will be 4

when the rate of interest is 10% forever after 10years will have effective interest as

=10.38% per year

interest balance will be $1000 if the initial balance is

where ER= effective interest calculated above

now prior to the withdrawl of 1000 every year the balance would be

1000+9632.72

10632.72

Now, the initial effective rate of interest per year for the first 10 years when rate of interest is 9% will be as

=9.308%

Now, the initial deposit will be calculated as the discount value of the account balance as

=9727.27

Hence, $9727.27 must be deposited to support the annual withdrawl of $1000 forever.