Final answer:
Paula should deposit approximately $83,204.88 into an account with a 1.07% interest rate, compounded monthly, to save $95,000 in 13 years.
Step-by-step explanation:
To determine how much Paula should deposit now into an account to achieve her goal of buying a $95,000 condominium in 13 years, we need to use the formula for the present value of a lump sum with compound interest. The formula is as follows:
PV = FV / (1 + r/n)^(nt)
- PV = Present value (the amount Paula needs to deposit now)
- FV = Future value (the amount needed in the future, which is $95,000)
- r = Annual interest rate (1.07% or 0.0107 as a decimal)
- n = Number of times interest is compounded per year (monthly compounding means n = 12)
- t = Number of years the money is invested (13 years)
Plugging these values into the formula:
PV = $95,000 / (1 + 0.0107/12)^(12*13)
PV = $95,000 / (1.00089167)^156
PV = $95,000 / 1.1421662821
PV ≈ $83,204.88
So Paula should deposit $83,204.88 now to reach her goal in 13 years.