Suppose you want to save $80,000 to put toward a down payment on a house in 7 years. How much will you need to deposit now if you can obtain an APR of 3.6% compounded quarterly? Assume that you make no deposits into the account after the initial deposit. (Round your final answer to the nearest cent.)
To calculate the initial deposit required to save $80,000 in 7 years with an APR of 3.6% compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($80,000 in this case)
P = the principal amount (initial deposit)
r = the annual interest rate (3.6% or 0.036 in decimal form)
n = the number of times the interest is compounded per year (quarterly, so 4 times)
t = the number of years the money is invested for (7 years)
Let's plug these values into the formula:
$80,000 = P(1 + 0.036/4)^(4*7)
First, let's simplify the exponent:
$80,000 = P(1 + 0.009)^28
Now, let's calculate the value inside the parentheses:
$80,000 = P(1.009)^28
Next, raise 1.009 to the power of 28:
$80,000 = P(1.272077)
Finally, divide both sides by 1.272077:
P = $80,000 / 1.272077
P ≈ $62,896.60
Therefore, you would need to deposit approximately $62,896.60 now to save $80,000 in 7 years with an APR of 3.6% compounded quarterly.