today you have $100,000 in your investment account, which will grow by 7.5% annually. if you keep investing…

today you have $100,000 in your investment account, which will grow by 7.5% annually. if you keep investing $600 every month, how many months does it take for your account balance to increase to $300,000? (report an integer)\nquestion 25\n5 pts\nif your total assets equal $14,743 and your total liabilities equal $14,253; your solvency ratio is: (keep 2 decimal places)\nquestion 26\n5 pts\nyour investment advisor wants you to purchase an annuity that will pay you $92,441 after 10 years. if you require a 6.7% return, what is the most you should pay for this investment? (keep 2 decimal places)

today you have $100,000 in your investment account, which will grow by 7.5% annually. if you keep investing $600 every month, how many months does it take for your account balance to increase to $300,000? (report an integer)\nquestion 25\n5 pts\nif your total assets equal $14,743 and your total liabilities equal $14,253; your solvency ratio is: (keep 2 decimal places)\nquestion 26\n5 pts\nyour investment advisor wants you to purchase an annuity that will pay you $92,441 after 10 years. if you require a 6.7% return, what is the most you should pay for this investment? (keep 2 decimal places)

Answer

Explanation:

Step1: Recall solvency - ratio formula

The solvency - ratio formula is $Solvency\ ratio=\frac{Total\ assets}{Total\ liabilities}$.

Step2: Substitute given values

Given total assets = $14743$ and total liabilities = $14253$. Then $Solvency\ ratio=\frac{14743}{14253}$.

Step3: Calculate the ratio

$Solvency\ ratio=\frac{14743}{14253}\approx1.03$.

Answer:

$1.03$

Explanation:

Step1: Recall present - value of a single - future - amount formula

The present - value formula for a single future amount is $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Identify the values

$FV=$92441$, $r = 0.067$, and $n = 10$.

Step3: Calculate the present value

$PV=\frac{92441}{(1 + 0.067)^{10}}=\frac{92441}{1.067^{10}}$. $1.067^{10}\approx1.908877$. $PV=\frac{92441}{1.908877}\approx48426.73$.

Answer:

$48426.73$

For the first part of the problem (growing investment account to a certain amount), we can use the future - value of a lump - sum and an ordinary annuity formula. Let $PV = 100000$, $PMT=600$, $r=\frac{0.075}{12}$, and $FV = 300000$. The future - value formula for a lump - sum and an ordinary annuity is $FV=PV(1 + r)^n+PMT\frac{(1 + r)^n-1}{r}$. Let $x=(1 + r)^n$, where $r=\frac{0.075}{12}=0.00625$. The equation becomes $300000 = 100000x+600\frac{x - 1}{0.00625}$. $300000=100000x + 96000x-96000$. $300000 + 96000=(100000 + 96000)x$. $396000 = 196000x$. $x=\frac{396000}{196000}\approx2.0204$. Since $x=(1 + 0.00625)^n$, then $n=\frac{\ln(x)}{\ln(1 + 0.00625)}=\frac{\ln(2.0204)}{\ln(1.00625)}$. $\ln(2.0204)\approx0.7037$, $\ln(1.00625)\approx0.00623$. $n=\frac{0.7037}{0.00623}\approx113$.

Answer:

$113$