As a rough guide to double any amount compounded annually, divide 70 by the interest rate. In this case that is 14 years.
Approximately 7 years. The general rule is to divide 70 by the interest rate to get an approximation of how long it will take to double. If the interest is compounded annual you will have $194.88 after 7 years, and $214.37 after 8 years. Though if interest is compounded more regularly (ie. monthly or daily) this will grow at a slightly faster rate.
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 .
y = ln(3)/ln(1.0575) = 19.65 years, approx.
Nine years at 8%
8.0432 years (rounded) if compounded annually.
As a rough guide to double any amount compounded annually, divide 70 by the interest rate. In this case that is 14 years.
4 years exactly.
Six years at 12%
Approximately 7 years. The general rule is to divide 70 by the interest rate to get an approximation of how long it will take to double. If the interest is compounded annual you will have $194.88 after 7 years, and $214.37 after 8 years. Though if interest is compounded more regularly (ie. monthly or daily) this will grow at a slightly faster rate.
Use the "rule of 72"...simply put, using compound interest you take the number 72 and divide it by the interest rate. Thus, at 5% the time to double is 14.4 years. This formula can be used for calculating a "double" for any interest rate using the same mathematical procedure.
Five years
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 .
The basic equation for compounded interest is: FV=PV(1+i)^nt FV=future value PV=present value i=interest compounded per term n=number of times compounded per year t=number of years For this situation: FV=? PV=8000 i=.08 n=1 t=7 Plugging the numbers into the equations gives you FV=8000(1+.08)^7 Solving gives you the amount of 13710.59 A way to roughly check your answer is to use the rule of 72. The rule of 72 is a method of seeing how long it would take to double ones money at a certain interest percent. The interest is 8% so divide 72 by 8 and you get 9. So at 8 percent it would take about 9 years to double your money. Since we only had 7 years, it makes sense that we did not double our money, but we fairly close to doing so, meaning that our answer is viable. This is only a way to roughly check the answer.
18 years. Let us say you deposit $1000 today @ 4% rate of interest compounded annually, you will have $1040 at the end of year 1. Similarly you'll have the following amounts year wise. 1 1040 2 1081.6 3 1124.864 4 1169.859 5 1216.653 6 1265.319 7 1315.932 8 1368.569 9 1423.312 10 1480.244 11 1539.454 12 1601.032 13 1665.074 14 1731.676 15 1800.944 16 1872.981 17 1947.9 18 2025.817 So, at the end of year 18 you will have $2025.817 which is more than double of what you deposited on year 1.
Using the compound interest formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years, we can solve for t when A = 4000, P = 2000, r = 0.06, and n = 1. Plugging these values in, we get: 4000 = 2000(1 + 0.06/1)^(1t) 2 = (1 + 0.06/1)^(1t) 2 = (1.06)^t Taking the logarithm of both sides, we can solve for t: log 2 = t log 1.06 t = log 2 / log 1.06 Using a calculator, we find that t is approximately 11.90. Therefore, it would take approximately 12 years to double the initial amount of 2000 at a 6 percent interest rate compounded annually.
If compounded, it will take 21.818 years.