If you start with an investment of I and the interest rate is r% per annum (compounded), then you want a solution to
2I = I(1 + r/100)24
or I = (1 + r/100)24
That is ln(2) = 24*ln(1 + r/100)
so that ln(1 + r/100) = ln(2)/24 = 0.02888
or (1 + r/100) = exp(0.02888) = 1.0293
and so r/100 = 0.0293 so that r = 2.93%
If you start with an investment of I and the interest rate is r% per annum (compounded), then you want a solution to
2I = I(1 + r/100)24
or I = (1 + r/100)24
That is ln(2) = 24*ln(1 + r/100)
so that ln(1 + r/100) = ln(2)/24 = 0.02888
or (1 + r/100) = exp(0.02888) = 1.0293
and so r/100 = 0.0293 so that r = 2.93%
If you start with an investment of I and the interest rate is r% per annum (compounded), then you want a solution to
2I = I(1 + r/100)24
or I = (1 + r/100)24
That is ln(2) = 24*ln(1 + r/100)
so that ln(1 + r/100) = ln(2)/24 = 0.02888
or (1 + r/100) = exp(0.02888) = 1.0293
and so r/100 = 0.0293 so that r = 2.93%
If you start with an investment of I and the interest rate is r% per annum (compounded), then you want a solution to
2I = I(1 + r/100)24
or I = (1 + r/100)24
That is ln(2) = 24*ln(1 + r/100)
so that ln(1 + r/100) = ln(2)/24 = 0.02888
or (1 + r/100) = exp(0.02888) = 1.0293
and so r/100 = 0.0293 so that r = 2.93%
If you start with an investment of I and the interest rate is r% per annum (compounded), then you want a solution to
2I = I(1 + r/100)24
or I = (1 + r/100)24
That is ln(2) = 24*ln(1 + r/100)
so that ln(1 + r/100) = ln(2)/24 = 0.02888
or (1 + r/100) = exp(0.02888) = 1.0293
and so r/100 = 0.0293 so that r = 2.93%
(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.
The formula to calculate the present amount including compound interest is, A = P(1 + r/n)nt , where P is the principal amount, r is the annual rate expressed as a decimal , t is the number of years, and n is number of times per year that interest is compounded. 9500 = 7000(1 + r/12)^(12 x 3) = 7000(1 + r/12)^36 Then, (1 + r/12)^36 = 9500 / 7000 = 1.3571429 approx (1 + r/12) = 36√1.3571429 ≅ 1.0085189 r/12 = 0.0085189 r = 12 x 0.0085189 ≅ 0.1022268 Then the required interest rate is 10.223% (3dp)
A well-structured problem has all the required information to solve it.
A well-structured problem has all the required information to solve it.
Equalizing connections are required when parallelingtwo compound generators and paralleling two Series generator .
Approx 44.225 % The exact value is 100*[3^(1/3) - 1] %
It is approx 8.66%
(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.
390.45
(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
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.
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!
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 %
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.
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
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