You have your choice of two investment accounts. Investment A is a 7-year annuit

Question

You have your choice of two investment accounts. Investment A is a 7-year annuity that features end-of-month $3,300 payments and has an interest rate of 7 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 9 percent, also good for 7 years.

How much money would you need to invest in B today for it to be worth as much as Investment A 7 years from now? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

You have your choice of two investment accounts. Investment A is a 7-year annuity that features end-of-month $3,300 payments and has an interest rate of 7 percent compounded monthly. Investment B is an annually compounded lump-sum investment with an interest rate of 9 percent, also good for 7 years.

Explanation / Answer

Investment A

Period = 7 years ; NPER = 7 years x 12 = 84

PMT = $3300

Rate = 7% compounded Monthly ; Rate per month = 7%/12 = 0.5833%

Present value of ordinary Annuity =

P = PMT [(1 - (1 / (1 + r)n)) / r]

Where:

P = The present value of the annuity stream to be paid in the future

PMT = The amount of each annuity payment

r = The interest rate

n = The number of periods over which payments are to be made

P = $3300 [(1 - (1/(1+.00583)84))/.00583

P = $218,649.04

Investment B

PMT = $3300 x 12 = $39,600

Period = 7 years

Rate = 9% compounded yearly

P = $39600 [(1 - (1/(1+.09)7))/.09

P = $199,304.93

b.

Future Value = Investment A = $218,649.04

Rate = 9%

Nper = 7 years

Present Value = Future Value/(1+ rate)^ nper

PV = $218,649.04/(1+ 9%)^7 = $119,608.51

Investment B = $119,608.51

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