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An initial investment of S3000 grows to S4500 in 9 years in an account that earns interest that is compounded continuously. Find the interest rate as a percentage r...

Question

An initial investment of S3000 grows to S4500 in 9 years in an account that earns interest that is compounded continuously. Find the interest rate as a percentage rounded to the nearest hundredth:

An initial investment of S3000 grows to S4500 in 9 years in an account that earns interest that is compounded continuously. Find the interest rate as a percentage rounded to the nearest hundredth:



Answers

Use the compound interest formulas $A=P\left(1+\frac{r}{n}\right)^{n t}$ and $A=P e^{n t}$ to solve.$ Round answers to the nearest cent. Suppose that you have $\$ 12,000$ to invest. Which investment yields the greater return over 3 years: $7 \%$ compounded monthly or $6.85 \%$ compounded continuously?

So in this problem we're being asked to use our compound interest formula as I know that you're on the right remember a represents the total in the account. He is the principle meaning the amount that was invested. R. Is the rate the percentage as a decimal and that's the number of times it gets compounded and t. Is the total duration. So if you're looking at our problem we're told $4,875 is invested. So that would be our p value. We're told that the rate is 1.8%. But we have to convert this to a decimal. So we move our decimal .2 places to the left which means we have 2.018. Now it's going to compound it quarterly which means four times a year. So and is equal to four and it's going to be an account for six years or sorry for nine years. So t would be nine. So now all we're going to do is substitute these values into our formula. So that will give us a equals p. Which is $4,875 times one plus R. Which is 0.18 Divided by N. Which is four. And it's getting raised to the end times team power. Well four times 9 is 36. So now you can go right to your calculator and type the sinuses and you'll get 5730 .235872. But remember the directions say to round to nearest set which means to places after the decimal? Well because that third places of five that means we have to bump that three up to a four. So the total amount in the account would be $5,730.24.

Okay, were given that we're compound it continuously with a rate of 9% and were asked how large miss our initial investment be in order to build 4000 or 50 K in seven years. You were looking for initial, which is peanuts. So what is that? Given that the world it's d que in seven years? Okay, Given a formula for compound continuously, that's PT is GOP not E r J, or interest rate is 9%. We're looking for P not, but we know that at seven years soapy of seven, this time seven, we received Christie 1000 dollars. Okay, Now we can solve the feet. Not so if we divide by, he's young 0.9 seven on both sides. And if you plug this into your calculator, you get approximately 26 6 to 9.59 This is our peanut. So this is how much we would need in order to get 50 K in seven years.

For this problem, we want to find the yearly interest rate Um that's earned by an investment that doubles in 10 years. So we have that is doubling in 10 years. So we have it's two times the initial investment may not and that's equal to a not E to the R. That's what we're trying to find. And it does that in 10 years. So because it's doubling, we go from me not to to A not, which means we just divide by a knot and reluctance to, then we can take the natural log of both sides. Natural log of E to anything is the anything we get rid of that base e. So now we have the natural log of two equals 10. Are so are is going to be the natural log of two divided by 10. But that tells us is that if we doubled our amount in 10 years, multiplying this time 200, we see that our interest rate must have been 6.9, or 6.9%, depending on how you around

Okay here we have a investment of $10,000 at 4% per year, compounded annually annually annually. And we're trying to find the amount after eight years. So looking are two formulas at the side. Our top formula is when we're given a annual rate, so that 4% per year means that we should be using the top formula. So our future value is going to equal that original $10,000 Multiplied by one plus. Now our rate as a decimal is going to be .04 and then we're compounding per year, so that's divided by one and then it's gonna be to the power of that one times than eight years. So that gives us a future value or a final amount for our investment Of $13,685.69.


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