Business, 12.10.2020 19:01 kekecantonxox121
Assume that you are 30 years old today, and that you are planning on retirement at age 65. You expect your salary to be $42,000 one year from now and you also expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 9%.
Required:
a. The present value (PV) (at age 30) of your retirement savings is .
b. A rich donor gives a hospital $1,040,000 one year from today. Each year after that, the hospital will receive a payment 6% larger than the previous payment, with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is
11%?
c. If the current rate of interest is 8%, then the present value (PV) of an investment that pays $1200 per year and lasts 24 years is closest to .
Answers: 2
![= \frac{P}{(r - g)}[1 - (\frac{(1 + g)}{(1 + r)})^n] \\](/tpl/images/0800/0258/78e65.png)
![=\frac{3,360}{(0.09 - 0.05)}[1 - (\frac{1.05}{1.09})^{35}]\\\\](/tpl/images/0800/0258/6b8da.png)
![=\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}](/tpl/images/0800/0258/a4c51.png)
![PV= [ \frac{P}{(r-g)}] \times [1-[\frac{(1+g)}{(1+r)}]^{n}]](/tpl/images/0800/0258/d8ef7.png)
![= [ \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](/tpl/images/0800/0258/60b69.png)
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