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Simple and compound interestBeing able to discount future cash flows using a compound interest rate is a critical skill.What is the present value of an investment that pays you $1,200 in 5 years’ time where annual interest rates are 8% compounded annually?$816.70$1,111.11$857.14$1,104.00

Question

Simple and compound interestBeing able to discount future cash flows using a compound interest rate is a critical skill.What is the present value of an investment that pays you 1,200in5years’timewhereannualinterestratesare81,200 in 5 years’ time where annual interest rates are 8% compounded annually?816.701,111.111,111.11857.14$1,104.00

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Solution

To calculate the present value of an investment that pays you $1,200 in 5 years’ time where annual interest rates are 8% compounded annually, you can use the formula for the present value (PV) of a future sum in compound interest, which is:

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

where:

  • FV is the future value of the investment, which is $1,200,
  • r is the annual interest rate, which is 8% or 0.08,
  • n is the number of times that interest is compounded per unit t, which is 1 time per year,
  • t is the time the money is invested for, which is 5 years.

Substituting these values into the formula gives:

PV = 1,200/(1+0.08/1)(1∗5)=1,200 / (1 + 0.08/1)^(1*5) = 1,200 / (1 + 0.08)^5 = 1,200/1.085=1,200 / 1.08^5 = 1,200 / 1.4693 = $816.30

So, the present value of the investment is approximately 816.30.Therefore,thecorrectansweris816.30. Therefore, the correct answer is 816.70 (due to rounding).

This problem has been solved

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