Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt...

Question

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have $12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

Accepted Answer

Hey everyone here we are asked to find which scenario will cause a greater return after five years. And beginning with part A. We see that we have 50.84%. That's compounded quarterly. So with this we need to recall the general compound interest formula which tells us that A. Is equal to P times the quantity of one plus R. Divided by N. To the power of N. Times T. And now here we need to identify each of our variables in this formula. So they will just be our total but P is going to be the principal amount which were given as $18,000. So 18,000 will be our p. And then our is our annual interest rate which we are told is 0.84%. And in decimal format this is 0.0084. And with this we can move on to finding n. Well N is the number of times the interest is compounded and we are told that is compounded quarterly. So this is four times a year and then T. Is the number of years which we are told is five. So T. Is just five. And now from here we can just plug in all of these values into our formula and find the return value. So we have A. Is equal to P which is 18,000 times the quantity of one plus R. Which is 0.84 divided by N. Which is four to the power of N which is four times T which is five. And now if we simplify this using a calculator, we find that A. Is equal to 18, 50.27. And this is an answer in a dollar amount. So now we can move on to finding the results of part B. So in part B we see that we have 0.81%. And this will be our our values we have R. is equal to 0.81%. And this industrial format is 0.0081. And now we are also told that is compounded continuously. So here we need to recall the when interest is compounded continuously. The formula is A. Is equal to p times E. To the power of R. T. And so we have our and we know that T. Is the same as part A. So T. Is five years and then we need to know P. Which we already have again Um from the initial statement of the problem. So P is 18,000 And now from here we just need to plug in this information. So you see that a. Is equal to p. Which is 18,000 times E. To the power of R. Which is 0.81 times T. Which is five. And now if you simplify this with your calculator, it comes with a pro an approximation where A. Is equal to 18, $0.96. And from here we just need to compare our two results so we see that part B is less than part A. So now we know that part A. Gives us a larger return. So our answer is part A. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have $12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

Key Concepts

Compound Interest

Compounding Frequency

Exponential Growth

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