Final answer:
To calculate the amount that must be deposited today into the account in order to have $45,000 in 38 years for a down payment on a house, we can use the formula for compound interest. by substituting the given values into the formula, we find that the amount that must be deposited today is approximately $9,982.42.
Step-by-step explanation:
To calculate how much must be deposited today into the account in order to have $45,000 in 38 years for a down payment on a house, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the future value (A) is $45,000, the annual interest rate (r) is 4%, and the time (t) is 38 years. Since the interest is compounded annually, n is 1. By substituting these values into the formula, we can solve for P:
A = P(1+r/n)^(nt)
$45,000 = P(1+0.04/1)^(1*38)
To solve for P, we isolate the variable:
P = $45,000 / (1+0.04/1)^(1*38)
Using a calculator or spreadsheet software, we can evaluate this expression to find that P, the amount that must be deposited today, is approximately $9,982.42.