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Teff = p%where the compounding js quarterly; what is the nominal rate?0A4[G8 +1)'_4] 0s4[(zoo - 1)'+4] C. 4[(zoo +1)*- 4]0.4 [(1o - 1)*+4]...

Question

Teff = p%where the compounding js quarterly; what is the nominal rate?0A4[G8 +1)'_4] 0s4[(zoo - 1)'+4] C. 4[(zoo +1)*- 4]0.4 [(1o - 1)*+4]

Teff = p% where the compounding js quarterly; what is the nominal rate? 0A4[G8 +1)'_4] 0s4[(zoo - 1)'+4] C. 4[(zoo +1)*- 4] 0.4 [(1o - 1)*+4]



Answers

Find the effective rate corresponding to each nominal rate.
4$\%$ compounded quarterly

Okay, discussion part A rate of interest is given 4.5% per year. Okay. And the amount is compounded monthly. Okay. Compounded monthly. And we have to find out the effective rate of interest. Okay? The formula of effective rate of interest is one plus r by m raised to the power m minus one. Okay. And when the compounded monthly then the convergent period for a year, it will be 12 times. Okay, So I will be 12. Now we will put the values so are effective. It will be one plus. Rate of interest is 4.5 that can be returned 4.5%. That is 0.45 divided by 12. Okay, raised to the power 12 minus one when we saw this. Okay. It will be 0.459 Or we can say 4.59% per year or per annum. And this will be the effective rate of interest for party of discussion. And now part B the rate of interest. The same 4.5% per year. Okay. And here the compounded daily, Okay. For the daily. Com foundation. Okay. We can say and will be 3 65. Now we will use the same formula. So are effective. It will be one plus again. Are by hair, M 0.45 divided by MLB 3 65 raised to the power and that is 3 65 minus one. Okay, So now when we saw this are effective in this case it will be 0.460 And when we say in the percentage it will be 4.60% per year. Okay. This will be the answer. A party of discussion. Thank you.

Okay. In discussion we able to find out the effective rate corresponding to the nominal rate. That is in the part a. Okay. six per year. And it is compounded compounded semi annually or we can say half yearly. Okay, So for half yearly can more than period will be M equals to two. Okay. And the nominal correspond nominal rate is given 6% per year and be able to find out the effective rate for the formula of effective rate is one plus r by am raised to the power m minus one. Okay. So effective that it will be our plus one plus R 6%. That is 0.6 divided by M. That is two raised to the power to minus one. And when we sold the effective rate with the calculator it will be 6.9% per year. Okay, this will be the answer. A party of discussion. And now we will move on the part B That is nominal rate is given 5%. Okay. Our is given 5%. Okay. And compounded quarterly. Okay. Compounded quarterly. So when compounded quarterly then the conversion period for a year. It will be four times. Okay. So I am well before and now we will use the same formula. Okay, that is here and we will put the values so Effective rate of interest. It will be one plus rate of interest. Are that is 0.05 divided by M that is four Raised to the Power four and -1. Okay. And it will be it will be 1.0125 raised to the power 4 -1. And when we stole using the calculator it will be 5.095 per year. Okay, so this will be the answer a part B of discussion. Thank you.

Problem Number four. The note is ableto 18 $8000. T is equal to 13 years and K is equal to 4.7 percent. So me is equal toe be note is 88 88,000 times e power, 4.47 Time 13 which is time to the final answer is 162 120

In this problem, we're looking at the compounded interest of an investment of $1000 the five year mark. So we're asked to find D. A. D. I. And here we're gonna use the chain rule. So we'll take our exponents. Bring it down. We'll keep the inside of our parentheses the same. And we'll subtract one from our exponents of this 19. But then we need to take the derivative of the inside here. So the derivative of one is zero and the derivative of I before is just 1/4. So we'll simplify this a little bit. And right now we have 20,000 over four times one was I over four to the 19th. So this simplifies to 5000 times one plus I over 4 to 19. And this represents the rate of change in annual interest after investing for five years. Where i is the interest rate.


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