Question

Suppose you start saving today for a 560,000 down payment that you plan to make on a houre in 6 yoars. Assume that you make no deposits into the account ater the intial deposit. For the account described below, how much would you have to deposi now to reach your 560,000 goal in 6 years An account wt daly compounding and an APR of 4%

Answer 1

Step-by-step explanation:

To calculate the amount you would need to deposit now to reach your goal of $560,000 in 6 years with daily compounding and an Annual Percentage Rate (APR) of 4%, we can use the formula for compound interest:

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

Where:

A is the future value (target amount) you want to reach ($560,000)

P is the principal amount (initial deposit) you need to determine

r is the annual interest rate (APR) in decimal form (4% = 0.04)

n is the number of compounding periods per year (365 for daily compounding)

t is the number of years (6)

Let's plug in the values and solve for P:

$560,000 = P(1 + 0.04/365)^(365*6)

Now, let's calculate it:

$560,000 = P(1 + 0.04/365)^(2190)

Divide both sides by (1 + 0.04/365)^(2190):

P = $560,000 / (1 + 0.04/365)^(2190)

Using a calculator, the approximate value for P is:

P ≈ $405,241.63

Therefore, you would need to deposit approximately $405,241.63 now to reach your goal of $560,000 in 6 years with daily compounding and an APR of 4%.