Answer: a deposit of $979.56 must be made now to have a balance of $1500 after 8 years with continuous compounding at 4.75% annual interest.
Step-by-step explanation: We can use the formula for continuous compounding:
A = Pe^(rt)
where A is the ending balance, P is the principal (initial deposit), e is the constant 2.71828..., r is the annual interest rate (as a decimal), and t is the time in years.
In this case, we know that A = $1500, r = 0.0475 (4.75% as a decimal), and t = 8 years. We want to solve for P.
P = A/e^(rt)
P = $1500/e^(0.0475*8)
P = $979.56 (rounded to the nearest cent)
Therefore, a deposit of $979.56 must be made now to have a balance of $1500 after 8 years with continuous compounding at 4.75% annual interest.