# Find the following values for a lump sum assuming annual compounding:The future value of \$500 invested at 8 percent for one yearThe future value of \$500 invested at 8 percent for five yearsThe present value of \$500 to be received in one year when the opportunity cost rate is 8 percent.The present value of \$500 to be received in five years when the opportunity cost rate is 8   percent.

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1. Find the following values for a lump sum assuming annual compounding:
• The future value of \$500 invested at 8 percent for one year
• The future value of \$500 invested at 8 percent for five years
• The present value of \$500 to be received in one year when the opportunity cost rate is 8 percent.
• The present value of \$500 to be received in five years when the opportunity cost rate is 8   percent.
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Step 1

Before we get into the solution, let's understand two reciprocal concepts:

If present value (PV) is known then we can calculate the future value (FV) making use of the following equation:

FV = PV x (1 + i)n

where i = interest rate / opportunity cost per period and

n = number of periods

We can invert the same equation to obtain PV if FV is known:

PV = FV x (1 + i)-n

Step 2

The future value of \$500 invested at 8 percent for one year = ?

Here, PV = \$ 500, i = 8%, n = 1

Hence, FV = 500 x (1 + 8%)1 = \$ 540

Step 3

The future value of \$500 invested at 8 percent for five years

PV = \$ 500, i =...

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