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Nominal and effective interest ratesBeing able to discount future cash flows using different compound frequencies is a critical skill.If you need $5,000 in 4 years’ time and your investment generate 6% interest per year, compounded semi-annually, how much do you need to put away today (i.e. what is the present value)?$3,947.05$3,960.47$3,137.06$4,716.98

Question

Nominal and effective interest ratesBeing able to discount future cash flows using different compound frequencies is a critical skill.If you need 5,000in4years’timeandyourinvestmentgenerate65,000 in 4 years’ time and your investment generate 6% interest per year, compounded semi-annually, how much do you need to put away today (i.e. what is the present value)?3,947.053,960.473,960.473,137.06$4,716.98

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Solution

To solve this problem, we need to use the formula for the present value of a future sum of money, which is:

PV = FV / (1 + r/n)^(nt)

where:

  • PV is the present value (the amount of money you need to put away today)
  • FV is the future value (the amount of money you want to have in the future, which is $5,000)
  • r is the annual interest rate (6% or 0.06)
  • n is the number of times the interest is compounded per year (semi-annually means twice a year, so n=2)
  • t is the number of years (4 years)

Substituting the given values into the formula, we get:

PV = $5,000 / (1 + 0.06/2)^(2*4)

Now, we just need to calculate the right side of the equation.

First, calculate the value inside the parentheses: 1 + 0.06/2 = 1.03

Then, raise this value to the power of 2*4 = 8: 1.03^8 = 1.2676506002282294

Finally, divide 5,000bythisvalue:5,000 by this value: 5,000 / 1.2676506002282294 = $3,947.05

So, the amount of money you need to put away today is approximately 3,947.05.Therefore,thecorrectansweris3,947.05. Therefore, the correct answer is 3,947.05.

This problem has been solved

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