Respuesta :
The Solution:
Let the present value of the investment be represented with P.
We shall use the formula below:
[tex]\begin{gathered} A=P(1+\frac{r}{100\alpha})^{n\alpha} \\ \text{Where} \\ A=\text{amount (after 5years)}=\text{ \$7000} \\ r=rate\text{ (in \%)=6 \%} \\ n=\text{ number of years =5 years} \\ \alpha=\text{ number of periods per annum =12} \\ P=\text{ Principal = initial investment=?} \end{gathered}[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} 7000=P(1+\frac{6}{100\times12})^{(5\times12)} \\ \\ 7000=P(1+\frac{6}{1200})^{60} \end{gathered}[/tex]So,
[tex]\begin{gathered} 7000=P(1+0.005)^{60} \\ \\ 7000=P(1.005)^{60} \\ \text{Dividing both sides by 1.005}^{60},\text{ we get} \\ P=\frac{7000}{1.005^{60}}=\frac{7000}{1.348850153}=5189.605\approx\text{ \$5189.61 (518961cent)} \end{gathered}[/tex]Thus, the present value of the investment that will yield $7000 at the end of 5 years is $5189.61 (or 518961 cents )
Therefore, the correct answer is $5189.61 (or 518961 cents )
