Suppose you start saving today for a $30,000 down payment that you plan to make on a house in 8 years. Assume that you make no deposits into the account after the initial deposit. For the account described below, how much would you have to deposit now to reach you $30,000 goal in 8 years.

An account with daily compounding and an APR of 6%
You should invest?

Use same procedure as previous problem.

To determine how much you need to deposit now in order to reach a $30,000 goal in 8 years with an account that offers daily compounding and an APR (Annual Percentage Rate) of 6%, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the account (which in this case is $30,000)
P = the initial deposit (the amount you need to find)
r = the annual interest rate (6%, which is written as 0.06 in decimal form)
n = the number of times interest is compounded per year (since the account offers daily compounding, this would be 365)
t = the number of years (8 in this case)

Now let's rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

Substituting the known values:

P = $30,000 / (1 + 0.06/365)^(365*8)

Calculating this using a calculator or spreadsheet, you will find that you need to deposit approximately $19,736.18 now in order to accumulate $30,000 in 8 years with daily compounding and an APR of 6%.