Suppose you need $500 in 9 months. How much must you deposit today, if the deposit will earn interest at 6% per year, compounded monthly?
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A. B. C. D. E.B
On the BAII Plus, press 9 N, 6 divide 12 = I/Y, 0 PMT, 500 FV, CPT PV. On the HP12C, press 9 n, 6 ENTER 12 divide i, 0 PMT, 500 FV, PV. Make sure the BAII
Plus has the P/Y value set to 1.
To calculate the amount you need to deposit today, we can use the concept of present value (PV) and the formula for compound interest.
The formula for compound interest is given by:
PV = FV / (1 + r/n)^(n*t)
Where: PV = Present Value (amount to be deposited today) FV = Future Value (amount needed in the future) r = Annual interest rate (in decimal form) n = Number of compounding periods per year t = Number of years
In this case, the future value (FV) is $500, the annual interest rate (r) is 6% (or 0.06 in decimal form), and the compounding period (n) is monthly. The time period (t) is given as 9 months, so we need to convert it to years by dividing it by 12 (since there are 12 months in a year).
Let's plug in the values into the formula:
PV = $500 / (1 + 0.06/12)^(12*(9/12))
Simplifying the equation:
PV = $500 / (1.005)^(9)
Using a calculator or spreadsheet, we can calculate the value inside the parentheses:
(1.005)^(9) = 1.045422
Now, substitute this value back into the equation:
PV = $500 / 1.045422
Calculating the present value:
PV ≈ $478.05
Therefore, the correct answer is B. $478.05.