Respuesta :
Answer:
The answer to this question can be defined as follows:
In point a, answer is "$61,303".
In point b, answer is " $7,681,257.74".
In point c, answer is "$12,635".
Explanation:
Given value:
In point a:
Year 1 = 0.08(42,000)
= $3,360
Time = 30 years
Rate Of Growth = 5%
Rate Of Interest = 9%
Formula:
Present Value [tex]= \frac{P}{(r - g)}[1 - (\frac{(1 + g)}{(1 + r)})^n] \\[/tex]
[tex]=\frac{3,360}{(0.09 - 0.05)}[1 - (\frac{1.05}{1.09})^{35}]\\\\[/tex]
[tex]=\frac{3,360}{(0.04)}[1 - (0.270207895)]\\\\=\frac{3,360}{(0.04)}[ 0.729792105]\\\\=\frac{2452.10147}{(0.04)}\\\\= 61,302.5368 \\\\ = \bold{61,303}[/tex]
In point b:
[tex]PV= [ \frac{P}{(r-g)}] \times [1-[\frac{(1+g)}{(1+r)}]^{n}][/tex]
[tex]= [ \frac{1,040,000}{(11 \%-6\% )}] \times [1-[\frac{(1+6 \% )}{(1+11 \%)}]^{10}] \\\\= [ \frac{1,040,000}{(5 \%)}] \times [1-[\frac{1.06}{(1.11)}]^{10}] \\\\= [ \frac{1,040,000}{(5 \%)}] \times [1-[(0.954954955)]^{10}] \\\\= [ \frac{1,040,000}{(5 \%)}] \times [1- 0.630708763] \\\\= [ \frac{1,040,000}{(5 \%)}] \times 0.369291237\\\\= [ \frac{1,040,000}{(5 \%)}] \times 0.369291237\\\\= 20800000 \times 0.369291237 \\\\= 7,681,257.74[/tex]
In point c:
[tex]PV= \frac{PMT \times (1- \frac{1}{1+r^n})}{r}\\[/tex]
[tex]= \frac{1200 \times 1- (\frac{1}{1.08^{24}})}{0.08}\\\\= \frac{1200 \times 1- (0.157699337)}{0.08}\\\\= \frac{1200 \times 0.842300663}{0.08}\\\\= \frac{1010.7608}{0.08}\\\\=12634.51\\\\= \bold{12635}[/tex]
