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How many years will it take to exhaust an IRA of $190000 if you withdraw $2000 every month? Assume a rate of interest of 7% compounded monthly....

Question

How many years will it take to exhaust an IRA of $190000 if you withdraw $2000 every month? Assume a rate of interest of 7% compounded monthly.

How many years will it take to exhaust an IRA of $190000 if you withdraw $2000 every month? Assume a rate of interest of 7% compounded monthly.



Answers

How many years will it take for an initial investment of $\$ 25,000$ to grow to $\$ 80,000 ?$ Assume a rate of interest of $7 \%$ compounded continuously.

Question. We're asked how long it will take to generate an amount of $80,000 given a principle investment $25,000 at a rate of 7% since its continuous from other issues. This formula or a is the amount after T years. Peas principal investment. He's just a constant our rate of interest and t It's a number of years. First we're going to do is write out old information. Given P is equal to 25 $25,000 A is equal to a $1000. And are you? So now you're plugging all this information into our creation? It's a 1000 as you could. 25 doesn't eat power. So you're saying Go ahead, divide 25,000 over, which would give us 32 physical e the power of 07 t. Now we're just gonna take the Ellen both size to isolate the T eat team, which will give us Ellen stupid too. One point 1 63 is equal to your parents. You seven g. Since this comes front, then heat, which is a good one, cancels out. So now you're seeing divides your printer sent over to get t equals 2.163 over you, which is equal to 16 but six one years. That's fine.

So let's consider we have a principal amount of $25,000 that's borrowed at a rate off 7%. Um, and we have that are net amount after tea years is $80,000. So, um, we're gonna use here our formula for compound interest, the amount after tea years A is equal to while the principal p times e raised to the r T power where our is our interest rates and t is the time in years so I could think of this As you know, the amount we have the two years is equal to pert, right? P times e to the r t. So here, um, we're trying to find the value of tea. We take our aid. The amount we have after tea years is 80,000. So $80,000 we have 80,000 is equal to the principle, which is 25 1000 times e raised to the rt. Well, our is 7%. So that 0.7 times t okay. What to solve this fatigue? What do we do? We divide both sides by 25,000 and then we take to get the tea. We have e raised to a power to take the natural log off both sides within. Bring tea out front, and then we can go ahead and south for tea and we get that t here is gonna be equal to approximately 16 point 61 years, right?

Again this question we have to find out how long will it take. It means we have to find out the time period. How long will it take an investment of $6000? That is peace given $6000 to grow to $7000. So accumulated values given also $7000. If the investment aren't interested the rate of 7.5% per year. So our is given 7.5% per year. Okay so it is in percent we can say it will be 0.75 Okay And we have to find out we will if the interest compounded continuously. Okay So if the interest compounded continuously we have to find out the time period. So no problem. If the interest compounded continuously, the formula of accumulated value is a cost to P. E. Raised to the power artie. And now we will put all the values that we have a 7000 P. 6000. And it is to the power Rt are is we have 0.75 and t is unknown. So now we have to find out the value of T. No problem. First of all, we will make it simple and we will divide both out of the question by 6000. So it will be 7000 divided by 6000 equals to be raised to the power 0.75 P. And now we can say it will be raised to the power 0.75 T equals to 7000 by 6000 weekend, simply say seven by six. Okay. And now we have to find out the value of the that is in the exponents. So we will take natural logarithms in the boats out of the question and it will be Ln he raised to the power 0.75 T equals two Ln seven by six. No problem. And now we know the property of logarithms that Ln areas to the power be. It will be B L N A. So it will be 0.75 T l n E equals two Ln seven by six. And now natural logarithms has the base E. So Ln base E. It will be one. So we can say 0.75 T. It will be Ln seven by six. And now we have to find out the value of T. So we will divide both sides of the question. But this 0.75 and T will be Ln seven by six divided by 0.75 And when we use the calculator and we solve this, it will be approximately 2.6 years. Okay. And this will be the final answer of our question. Thank you.

Equals P rt. The I stands for the interest, which is the amount of money you are earning or Winter P stands for the principle, which is the amount of money you're putting down R stands for the rate which we use. The percent were given, and we write it as a decimal and T stands for the amount of time now in this problem, we know we want to earn $252 in interest. So I'm going to put that where the eye is. So I will have 252 equals, and we know that we're investing $2400. So I'm going to put that where the P waas and I'm going to put it in parentheses since I'm going to be multiplying and I know I'm multiplying because when I have three variable smushed together like I do p r t, that means P times are times T. We're also told that it's invested at a 7% interest, so I'm going to write 7% as a decimal, which is 70.7 If you're ever not sure how to write a percent as a decimal, you can just divide the process by 100. And what we're being asked to find is the time. How much time? How long will it take? Some going to leave the tea there. So now you can see I have the equation. 252 equals 2400 times 24000.7 So the first thing I'm going to do is the 2400 times 24000.7 which is equal to 168. And then I'm gonna bring down the tea. And I'm still going to have the equals 252 now to solve for T, which is time I have to get rid of this 168 toe. Isolate the T variable. So I use inverse operations to do this and versus just a fancy way to say opposite. So I asked myself first what's happening between the 168 and T. And that's 168 times t. So then I asked myself, What is the inverse or opposite of multiplying by 1 68 and that would be dividing? When I do that, I can cross out the to 160 eights because 168 divided by 168 is just one. And when I write T, it's automatically assumed that the coefficient is one. So we're basically saying Won t and we don't actually have to write the one. So I have my tea and I have my equal sign And now, because of properties of equality, if I divide by 168 on one side, I have to divide by 168 on the other and 252 divided by 168 is 1.5. So I get that. The amount of time it will take is 1.5, and that's in years, because time when using the I equals P RT formula is always measured in years, so it will be 1.5 or 1.5


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