Question

question 21 (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) $840.00
c) $871.44
d) $870.41

Explanation:

Step1: Identify compound - interest formula for present value

The formula for present value $PV$ when compounded $n$ times a year 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 $FV = 1000$, $r=0.035$ (since $3.5\%=0.035$), $n = 2$ (semi - annual compounding), and $t = 4$.

Step3: Substitute values into the formula

$PV=\frac{1000}{(1+\frac{0.035}{2})^{2\times4}}=\frac{1000}{(1 + 0.0175)^{8}}$.
First, calculate $(1 + 0.0175)^{8}$. Using the formula $a^{n}=e^{n\ln(a)}$ or simply a calculator, $(1 + 0.0175)^{8}\approx1.14888$. Then $PV=\frac{1000}{1.14888}\approx870.41$.

Answer:

d) $\$870.41$