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It is approx 8.66%

Q: What interest rate is required for an investment with continuously compounded interest to double in 8 years?

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Approx 44.225 % The exact value is 100*[3^(1/3) - 1] %

(1+x)10 = 310 log(1+x) = log(3)log(1+x) = 0.1 log(3)(1+x) = 10[0.1 log(3)] = 1.116123x = .116123 = 11.61 percent

Future Value = (Present Value)*(1 + i)^n {i is interest rate per compounding period, and n is the number of compounding periods} Memorize this.So if you want to double, then (Future Value)/(Present Value) = 2, and n = 16.2 = (1 + i)^16 --> 2^(1/16) = 1 + i --> i = 2^(1/16) - 1 = 0.044274 = 4.4274 %

1). My money will never double. Let's talk about Jon's money instead. 2). It doesn't matter how much he deposits into the account. The time required for it to double is the same in any case. 3). At 8% interest compounded annually, the money is very very very nearly ... but not quite ... doubled at the end of 9 years. At the end of the 9th year, the original 1,000 has grown to 1,999.0046. If the same rate of growth were operating continuously, then technically, it would take another 2days 8hours 38minutes to hit 2,000. But it's not growing continuously; interest is only being paid once a year. So if Jon insists on waiting for literally double or better, then he has to wait until the end of the 10th year, and he'll collect 2,158.92 .

If it is compounded annually, then: F = P*(1 + i)^t {F is final value, P is present value, and i is interest rate, t is time}.So if it triples, F/P = 3, and 12 years: t = 12, so we have 3 = (1 + i)^12, solve for i using logarithms (any base log will do, but I'll use base 10):log(3) = log((1+i)^12) = 12*log(1+i)(log(3))/12 = log(1+i).Now take 10 raised to both sides: 10^((log(3))/12) = 10^log(1+i) = 1 + ii = 10^((log(3))/12) - 1 = 0.095873So a rate of 9.5873 % (compounded annually) will triple the investment in 12 years.

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Approx 44.225 % The exact value is 100*[3^(1/3) - 1] %

the equation for compound interest is Pe^(rt) the principal you want in the end is twice that of the original 12,000 plugging in and solving you get 12,000=6000e^(.13t) t = 5.33 years

(2)1/21 = 1.03356 (rounded)That's an annual interest of 3.356 percent.Let's try it:(1.03356)21 = 2.00009 on my calculator, which is pretty close.

We still need to know how often the interest is compounded ... Weekly ? Daily ? Hourly ? What does "continuous" mean ?

A good jumbo CD rate would be over 5% and one must be careful to find out how often the interest will be compounded. Also important is the minimum investment amount that would be required.

Solve the following equation: (1 + x/100)8 = 3. That is, your money increases by a certain factor each year; the factor is the capital plus the percentage rate (divided by 100), and if you multiply the factor by itself 8 times, you get a factor of 3. To start solving this, take the 8th. root left and right.

3.73% would do it almost exactly: Where p is the original investment and i is the rate of interest: 3p = p((1 + i/100) to the power of 30) dividing by p gives ((1 + i/100) to the power 30) = 3 using logarithms (log 3)/30 = 1 + i/100 antilog (0.47712/30) = 1 + i/100 antilog 0.0159 = 1 + i/100 1.037299 = 1 + i/100 0.037299 = i/100 i = 3.7299 Later: I tested this on Excel with capital of 5000 and interest rate of 3.73% and after 30 years investment was worth 15000.35!

(1+x)10 = 310 log(1+x) = log(3)log(1+x) = 0.1 log(3)(1+x) = 10[0.1 log(3)] = 1.116123x = .116123 = 11.61 percent

390.45

required rate of return is the 'interest' that investors expect from an investment project. coupon rate is the interest that investors receive periodically as a reward from investing in a bond

Future Value = (Present Value)*(1 + i)^n {i is interest rate per compounding period, and n is the number of compounding periods} Memorize this.So if you want to double, then (Future Value)/(Present Value) = 2, and n = 16.2 = (1 + i)^16 --> 2^(1/16) = 1 + i --> i = 2^(1/16) - 1 = 0.044274 = 4.4274 %

1). My money will never double. Let's talk about Jon's money instead. 2). It doesn't matter how much he deposits into the account. The time required for it to double is the same in any case. 3). At 8% interest compounded annually, the money is very very very nearly ... but not quite ... doubled at the end of 9 years. At the end of the 9th year, the original 1,000 has grown to 1,999.0046. If the same rate of growth were operating continuously, then technically, it would take another 2days 8hours 38minutes to hit 2,000. But it's not growing continuously; interest is only being paid once a year. So if Jon insists on waiting for literally double or better, then he has to wait until the end of the 10th year, and he'll collect 2,158.92 .