Solve the problem.
-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 5% compounded semiannually, to yield $26,000?
A)$16,670.42
B)$23,097.31
C)$20,775.90
D)$20,905.81

Question

Solve the problem. 
-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 5% compounded semiannually, to yield $26,000?
A)$16,670.42 
B)$23,097.31 
C)$20,775.90 
D)$20,905.81

Quizplus · Accepted Answer

To find the present value (the lump sum to be invested today) that will yield $26,000 in 9 years at an interest rate of 5% compounded semiannually, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value ($26,000), r is the interest rate per period (5% per year or 0.05, divided by 2 for semiannual compounding, so 0.025), and n is the total number of compounding periods (9 years times 2, so 18 periods). Plugging in the values, we get $PV = \frac{26,000}{(1 + 0.025)^{18}}$, which calculates to approximately $16,670.42.

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