Question

# What is most nearly the present worth of \$27,000 due in 6 years if the interest...

What is most nearly the present worth of \$27,000 due in 6 years if the interest rate is 13% per year, Compounded semi-annually?

Select the correct Option:

(a) \$4,000

(b) \$6,000

(c) \$13,000

(d) \$24,000

The correct OPTION is "C" \$13,000

Given Data,

Amount = \$27,000

Time = 6 years

Rate of interest = 13%

Here, we have to find the most nearly the present worth of the given data which can be found by the following formula:-

P = F (1 + i)-n

Where,

P = Present worth = TO FIND

F = \$27,000

i = 6.5% = 0.065

as it is Clearly Given "Compounded semi-annually"

So, (13%per year) / 2 periods per year = 6.5% = 0.065

n = 12 Periods

(6 years) * 2 periods per year = 12 Periods

Compounded Semi-annually

Substituting the respective value in the Formula

P = F (1 + i)-n

P = \$27,000 (1 + 0.065)-12

P = \$27,000 * (0.46968285439)

P = \$12,681

So, the most nearly Option provided in the question is \$13,000

The correct OPTION is "C" \$13,000

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