Answer:
$2398.52
Step-by-step explanation:
The amortization formula can be used to find the principal amount that is required to support payments of $10,000 per quarter.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
A is the periodic payment, P is the principal amount, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
10,000 = P(.08/4)/(1 -(1 +.08/4)^(-4·10)) = .02P/(1 -1.02^-40)
P = 10000(1 -1.02^-40)/.02
P = $273,554.79 . . . . . balance required when payouts start
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The annuity formula can be used to find the periodic payment required to achieve this balance.
A = P((1 +r/n)^(nt) -1)/(r/n)
A is the sum of the payments P made n times per year. Interest rate r is also compounded n times per year for t years.
273,554.79 = P((1 +.08/4)^(4·15) -1)/(.08/4) = P(1.02^60 -1)/.02 = 114.05154P
273,554.79/114.05154 = P = 2398.52
Mike must deposit $2398.52 quarterly to accomplish his goal.
