What deposit today is needed to have $2,000 in 4 years, assuming the money will earn interest at 6% per year, compounded monthly?
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A. B. C. D. E.C
On the BAII Plus, press 48 N, 6 divide 12 = I/Y, 0 PMT, 2000 FV, CPT PV. On the HP12C, press 48 n, 6 ENTER 12 divide i, 0 PMT, 2000 FV, PV. Make sure the
BAII Plus has the P/Y value set to 1.
To calculate the deposit needed to have $2,000 in 4 years with an interest rate of 6% per year, compounded monthly, we can use the future value of a lump sum formula:
FV = PV * (1 + r/n)^(n*t)
Where: FV = Future value ($2,000) PV = Present value (deposit) r = Annual interest rate (6% or 0.06) n = Number of compounding periods per year (12, since it's compounded monthly) t = Number of years (4)
We need to solve for PV, so let's rearrange the formula:
PV = FV / [(1 + r/n)^(n*t)]
Plugging in the given values:
PV = $2,000 / [(1 + 0.06/12)^(12*4)]
Calculating the inside of the parentheses:
PV = $2,000 / (1.005)^(48)
Using a calculator or spreadsheet, we find that (1.005)^(48) is approximately 1.263680799.
PV = $2,000 / 1.263680799
PV ≈ $1,581.32
Therefore, the deposit needed today to have $2,000 in 4 years, assuming the money will earn interest at 6% per year, compounded monthly, is approximately $1,581.32.
Among the given answer choices, the closest option is C. $1,574.20.