13.1 Using a combined interest rate per interest period (d) for computing presen

Question

13.1  Using a combined interest rate per interest period (d) for computing present worth values (PW), What is the present worth of the $1,000,000.00 you accumulated in Problem 12.2, if the formula for d is d = i + f + (i × f) and the inflation rate (f)=2.3%=0.023 (use the decimal equivalent in the formula) and the interest rate (i) is still 6%=0.06 (use the decimal equivalent in the formula) and n is the same as in Problem 12.2?

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12.2 Given your current age to the nearest month, (for example 24 years, 6 months 24.50) how much money would you need to pay into a mutual fund each month, starting now, in order to have $1,000,000.00 at age 59 ½, if the fund averages a 6% annual expected rate of return, compounded monthly, during that period of time? Given: F-$1,000,000, n-35 years-420 months, i-696-0.5%)monthly, A-PM-? A=$1,000,000(A/F, 0.5%, 420) A-s1.0,000[i/ (1-i)'-1) A-$1,000,000[i/ (1+i)-1)] A-$1,000.000o.0050 (1+0.005020-1)] A-$1,000,000[0.0050/ (1.0050)420-1)] A-$1,000,000[0.0050/ (8.123552)-1)] A-$1,000,000[0.0050 / (7.123552)] A-$1,000,000[0.000701897] A=$701.90 Excel Check: A-PMT (6%/12, 35*12,, 1000000), again, A-$701.90

Explanation / Answer

Interest rate per year = .06 + .023 + (.06*.023) = 8.438%

Number of periods = 35 years = 420 months

Monthly interest rate = 0.7032%

Present Value = $1,000,000/(1+.7032%)^420

= $52,709.21

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