Final answer:
To calculate how much Steven needs to invest in an account with a 5.8% interest rate compounded daily to save $48,000, we need to use the formula for compound interest and know the number of years he plans to invest (t). Without the time period, we cannot calculate the exact initial investment amount.
Step-by-step explanation:
Steven is interested in knowing how much he would need to invest initially to save $48,000 for a down payment on a home with an interest rate of 5.8% compounded daily. This question involves the concept of compound interest. The general formula for compound interest, when compounded daily, is A = P(1 + r/n)^(nt), where:
A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial deposit)
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the number of years the money is invested for
However, if we want to find out the principal amount P, we need to re-arrange the formula:
P = A / (1 + r/n)^(nt)
In Steven's case, to find out the amount he needs to invest, we substitute A = $48,000, r = 0.058, and n = 365 (compounded daily). However, we need one more piece of information: t, the number of years he plans to keep the money invested, which is not provided in the question.
Once Steven provides the number of years t, we can solve for P using the formula for compound interest to determine how much he will need to invest initially.