Question

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

Answer 1

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