Southwest Dry Cleaners believes that it will need new equipment in 9 years. The equipment will cost $26,000. What lump sum should be invested today at 12% compounded semiannually, to yield $26,000?
A) $9108.94
B) $15,440.52
C) $19,593.79
D) $15,212.33

Question

Quizplus · Accepted Answer

To find the present value (the lump sum to be invested today) that will grow to $26,000 in 9 years at a 12% annual interest rate compounded semiannually, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value ($26,000), r is the annual interest rate (12% or 0.12), n is the number of compounding periods per year (2 for semiannual), and t is the time in years (9). Plugging in the values, we get $PV = \frac{26,000}{(1 + 0.12/2)^{2*9}}$, which calculates to approximately $9108.94.

Southwest Dry Cleaners Believes That It Will Need New Equipment