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You have your choice of two investment accounts. Investment A is a 9-year annuity that features end-of-month $1,780 payments and has an interest rate of 9 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 11 percent, also good for 9 years.

Question

You have your choice of two investment accounts. Investment A is a 9-year annuity that features end-of-month $1,780 payments and has an interest rate of 9 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 11 percent, also good for 9 years.

check_circleAnswer
Step 1

All financials below are in $.

Characterisitics of Investment A:

  • Monthly annuity, M = 1,780
  • Frequency is monthly; hence period is month
  • Interest rate per period, R = 9% / 12 = 0.75%
  • Number of periods, N = no. of months in 9 years = 12 x 9 = 108

FUture value of this annuity at the end of 9 years will be given by FV as shown on white board.

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Step 2

Investment Characteristics of B:

  • One time lumpsum payment
  • Annual interest rate, i = 11%
  • Number of years, T = 9

Let's assume the lumsum amount be L. Hence, it's future value must be same as FV calculated in earlier step.

Step 3

Hence, Future value of L = FV

Hence, L x (1 + i)T = L x (1 + 11%)9 = 2.5580 ...

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