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Brief Exercise 6-2 Steve Bautista needs $28,800 in 4 years. Click here to view factor tables...

Brief Exercise 6-2

Steve Bautista needs $28,800 in 4 years.

Click here to view factor tables

What amount must he invest today if his investment earns 8% compounded annually? What amount must he invest if his investment earns 8% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment at 8% annual interest $

Investment at 8% annual interest, compounded quarterly $

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Answer #1

(a)-Amount to be invested today if the Investment earns 8.00% annual interest

Here, we’ve Future Value = $28,800

Annual interest rate (r) = 8.00% per year

Number of years (r) = 4 Years

Therefore, the Present Value = Future Value / (1 + r)n

= $28,800 / (1 + 0.08)4

= $28,800 / (1.08)4

= $28,800 / 1.36049

= $21,169

(b)-Amount to be invested today if the Investment earns 8.00% annual interest compounded quarterly

Here, we’ve Future Value = $28,800

Quarterly interest rate (r) = 2.00% [8.00% / 4]

Number of years (r) = 16 Years [4 Years x 2]

Therefore, the Present Value = Future Value / (1 + r)n

= $28,800 / (1 + 0.02)16

= $28,800 / (1.02)16

= $28,800 / 1.37279

= $20,979

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