Suppose you need $800 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.B
On the BAII Plus, press 20 N, 8 divide 12 = I/Y, 0 PMT, 800 FV, CPT PV. On the HP12C, press 20 n, 8 ENTER 12 divide i, 0 PMT, 800 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 formula for future value of a lump sum investment:
FV=PV×(1+r)n
Where: FV = Future Value (the amount you need in the future) PV = Present Value (the amount you need to deposit today) r = interest rate per compounding period (in this case, the monthly interest rate) n = number of compounding periods
Given that you need $800 in 20 months, and the interest rate is 8% per year, compounded monthly, let's break down the information:
Future Value (FV) = $800 Number of compounding periods (n) = 20 months Interest rate (r) = 8% per year, compounded monthly
First, we need to convert the annual interest rate to the monthly interest rate. Since there are 12 months in a year, the monthly interest rate would be 8% divided by 12:
Monthly interest rate (r) = 8% / 12 = 0.08 / 12 = 0.00667 (rounded to 5 decimal places)
Now, we can plug these values into the formula and solve for the Present Value (PV):
$800 = PV × (1 + 0.00667)^20
To solve for PV, we need to isolate it on one side of the equation. Divide both sides of the equation by (1 + 0.00667)^20:
PV = $800 / (1 + 0.00667)^20
Using a calculator, we can evaluate the right side of the equation:
PV = $800 / (1.00667)^20 = $800 / 1.147854 = $697.72 (rounded to 2 decimal places)
Therefore, the amount you must deposit today is approximately $697.72.
None of the given answer options match the calculated result exactly. However, the closest option is answer B, $700.45.