Suppose you need $500 in 20 months. How much must you deposit today, if the deposit will earn interest at 8% per year, compounded monthly?
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A. B. C. D. E.Explanation
On the BAII Plus, press 20 N, 8 divide 12 = I/Y, 0 PMT, 500 FV, CPT PV. On the HP12C, press 20 n, 8 ENTER 12 divide i, 0 PMT, 500 FV, PV. Make sure the
BAII Plus has the P/Y value set to 1.
To solve this question, we can use the formula for calculating the future value of a lump sum investment with compound interest:
Future Value = Present Value × (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Number of Years)
In this case, we want to find the present value (the amount to deposit today) that will accumulate to $500 in 20 months. The interest rate is 8% per year, compounded monthly.
Let's break down the given information: Future Value = $500 Number of Years = 20 months ÷ 12 months/year ≈ 1.67 years Interest Rate = 8% per year Number of Compounding Periods = 12 (monthly compounding)
Now, we can plug these values into the formula:
$500 = Present Value × (1 + (0.08 / 12))^(12 × 1.67)
To solve for the present value, we need to isolate it on one side of the equation:
Present Value = $500 / (1 + (0.08 / 12))^(12 × 1.67)
Using a calculator, let's calculate this expression:
Present Value = $500 / (1 + (0.08 / 12))^20.04
Present Value ≈ $437.78
Therefore, the amount you must deposit today to accumulate $500 in 20 months, with an 8% annual interest rate compounded monthly, is approximately $437.78.
The correct answer is B. $437.78.