Question

question 12 (mandatory) (1 point) the present value of an investment that will be worth $1000 in 4 years at 3.5% per year compounded semi - annually is a) $1148.88 b) $871.44 c) $870.41 d) $840.00

Explanation:

Step1: Identify compound - interest formula for present value

The formula for present value $PV$ when compounded semi - annually is $PV=\frac{FV}{(1 + \frac{r}{n})^{nt}}$, where $FV$ is the future value, $r$ is the annual interest rate (in decimal), $n$ is the number of compounding periods per year, and $t$ is the number of years.

Step2: Determine the values of variables

Given $FV = 1000$, $r=0.035$, $n = 2$ (semi - annual compounding), and $t = 4$.

Step3: Substitute values into the formula

$PV=\frac{1000}{(1+\frac{0.035}{2})^{2\times4}}=\frac{1000}{(1 + 0.0175)^{8}}$.

Step4: Calculate $(1 + 0.0175)^{8}$

$(1 + 0.0175)^{8}=1.0175^{8}\approx1.1488$.

Step5: Calculate the present value

$PV=\frac{1000}{1.1488}\approx870.41$.

Answer:

c) $\$870.41$