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Calculate the future value of a savings account for a S600 quarterly deposit where annual interest is compounded quarterly at 5.6% for 3 years: (3)You decide that y...

Question

Calculate the future value of a savings account for a S600 quarterly deposit where annual interest is compounded quarterly at 5.6% for 3 years: (3)You decide that you want to have S100 000 in the bank 20 years from now: What will be your regular monthly deposits into a bank account that offers 3% annual interest compounded monthly: (3)Every six months, you deposit S750 into a charitable savings account that will pay 7% interest compounded semi-annually: How much is in the account in 4 years? How

Calculate the future value of a savings account for a S600 quarterly deposit where annual interest is compounded quarterly at 5.6% for 3 years: (3) You decide that you want to have S100 000 in the bank 20 years from now: What will be your regular monthly deposits into a bank account that offers 3% annual interest compounded monthly: (3) Every six months, you deposit S750 into a charitable savings account that will pay 7% interest compounded semi-annually: How much is in the account in 4 years? How much interest was earned? (4)



Answers

The amount of money, $A(t),$ in a savings account that pays $6 \%$ interest, compounded quarterly for $t$ years, with an initial investment of $P$ dollars, is given by $$ A(t)=P\left(1+\frac{0.06}{4}\right)^{4 t} $$
If $\$ 800$ is invested at $6 \%,$ compounded quarterly, how much will the investment be worth after 3 yr?

Alright, so here I have kind of the setup for this problem, we have our information in black, they gave us 3% per year that we're going to grow in this fund and it's compounded semi annually. We wanted to result in $5,000 after about a year. So we're going to use the compounding interest formula here. A is the final amount. P is the starting amount times one plus R. Is the rate divided by the number of times compounded raised to the number of times compound at times T. So n happens twice in this formula 3% rate. That's my are. But I'm going to use .03 semi annually means I'm cutting this in half. Like I'm compounding it twice a year. So I'm gonna use to for compound for the number of times is compounded. The goal is to get to 5000. So that's the a. And the time is one year. So I can set up this equation right here with all that information. and then at this point I can put everything on the calculator to be able to solve some. Just put one plus Point of three divided by two. And the order of operations will take care of that for me Race to the two times 1. So I get that decimal 1.3 oh 2-5. And I want to keep as many of those numbers as possible. I'm going to divide by that long decimal and that's going to get me my final answer that I need to accomplish. So this number is how much my original mounts can get, multiplied by over the course of the year To my back and press two with this negative button to get answer. And it's gonna copy that decimal in for me. So 8 4053 and 31 cents. And that is my answer.

So we're given the formula for amount after 30 years. Component Quarterly at 6% interest yes, A F p is equal to p times one plus 0.6 by four to the power 40. He's amount invested. He is the time in years. So we're giving piece $500 and he is two years. So monitors okay to the power for him to do it is approximately 5 63 $0.25.

In this question. We're looking at compound interest. So we go get our formula for compound interest, which is three amount Lee count is equal to the principal times one plus the interest rate divided by the number of compounds. And that quantity now has an exponents. We're gonna raise it to the number of compounds times the time in years. Next, we're gonna substitute. So in this question or principal amount is $2000. Our interest rate is 3%. So that's 30.3 Divided by the number of compounds they tell us it's quarterly. So that's gonna be four compounds, and then our number of compounds is four times the one year. Now we're ready to simplify. Remember, you need to work inside of the parentheses first, Then take care of that exponents. And then, lastly, will multiply the 2000 so that we get a total of $2060.68

We're working with compound interest now, so we go getter formula. We will need that formula. The amount in the account is equal to the principal times one plus the rate divided by the number of compounds raised to the number of compounds times the time Then we're ready to substitute are known values. So our principle is 3000. Our interest rate is 2%. So that's 20.2 This is calm, pounded quarterly. That means there's four compounds per year. Both those cases for the end well, places for and there today we're gonna have this for one year. So it's just times one. Now we're ready to simplify or do the math. Remember, we're gonna work inside those parentheses first and then do the exponents. And then the last thing we're gonna do is multiplied by that 3000 and do a rounding to the nearest penny. So our total value is $3060.45. Make that look a lot more like a desk


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