Problema Solution
Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000?
Answer provided by our tutors
P = the principal (lump sum to be invested)
r = 0.12 or12% annual interest rate
t = 8 years
n = 2*t = 2*8 = 16 compounding periods (the account is compounded semiannually)
A = $26,000 future value
A = P(1 + r/2)^n
P(1 + 0.12/2)^16 = 26000
P(1.06)^16 = 26000
by solving we find:
P = $10,234.80
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Great Dish should invest a lump sum of $10,234.80.