How much money must be invested into an account paying 4% annually, compounded a

Question

How much money must be invested into an account paying 4% annually, compounded annually, to have $635,000 in 29 years when I retire?

a) Calculate the PV (Present Value) using the “Present Value of $1.00” table in your textbook.

Remember: To use Table 13-3, you need the Number of Periods and the Interest Rate per Period.

b) Calculate the PV (Present Value) using the formula: PV = FV / (1 +R)N

Reminder: Always show work. You can do this by stating the values that you are substituting into the formula.

c) How much interest did you earn over the life of the investment?

You can use either the result from Part 4a or Part 4b for your calculations, since they are slightly different. Show your work.

Explanation / Answer

(A) Here time t = 29 years

Interest Rate = 4% annually

If we see the PV table the value for i = 4% and t = 29 years

so the present value of $1.00 = $0.3207

so THe money that shall be invested presently = 635000 * 0.3207 = $ 2,03,644.5

(b) Now by using formula

PV = FV / (1 + r)N

PV = 635000 / ( 1+ 0.04)29 = 635000 / 3.11685 = $ 2,03,613.65

(c) Interest earned over the life taking Part 4 a as answer = $ 6,35,000 - $ 2,03,644.5 = $4,31,355.5

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