How long will it take a sum of money to double at 5% per year?

Question

So, I know that if I multiply the original sum by 5%, or 1.05 I will know what I get in a year. But how do I figure how long it will take to double?

Answer 1

assuming that interest is paid only once a year at 5%, use the compound interest formula to find when it will double.

At = Ao(1+r/n)^nt

where r is the rate
n is the number of times per year money is compounded. in this case it is 1
t is the number of years
Ao is the original amount

2Ao = Ao(1+ .05)^t
2 = 1.05^t
ln2 = t ln 1.05
t = ln 2 / ln 1.05
= .693147 / .04879
t = 14.2067 years for money to double

a quick way to see if when your money will double is to divide 72 by the interest rate to get an approximate answer. so in this case it would be 72/5 = 14.4 years approximately

Answer 2

to double the amount u need 100% of the amount
say u have 10$ so u need 100% of 10$ to make it 20$

now interest is 5% per year. so how many years will make it 100% ? 100/5 = 20
so answer is 20 years !
this method uses the calculations as per simple interest
so as per compound interest the answer given by others is right

Answer 3

let's say the amount of money you put in is P

set the equation of interest equal to 2P (the amount you will end up with)

so 2P = P(1.05^t)

and plug the numbers in, then solve to get

2 = 1.05^t

then take the log of both sides to get

log2 = log1.05^t

use the exponent rule to bring it down to the front of the log

log 2 = tlog1.05

then divide by log1.05

to get t=log2/log1.05

which is 14.20669908

or 14.21 years

Answer 4

Depends on compounding. For simple interest
2=1+0.05t
0.05t=1
t=20 years
compounding annually
2=1.05^t
t*ln 1.02=ln 2
t=ln 2 /ln 1.05=14.2 years
compounding continouosly
2=e^0.05t
0.05t=ln 2
t=20* ln 2=13.86 years

Answer 5

Let S denote the initial sum of money.

S(1+.05)^t=2S
(1.05)^t=2
tln(1.05)=ln(2)
t=ln(2)/ln(1.05)=14.2067 years.

Answer 6

Make a table:
Let n be number of years, P be the principal

n (years) ; $

0 ; P
1; 1.05*P
2; (1.05)^2*P
3; (1.05)^3*P
...
n; (1.05)^n*P

So you want to find the n such that

(1.05)^n*P = 2*P
i.e.:
(1.05)^n = 2
solve for n by using logs:
n*log(1.05) = log(2)
n = log(2)/log(1.05)

Answer 7

x(1.05)^y=2x
x= original amount
y=number of years

Answer 8

ok....
say we deposit $1000
after one year at 5% it will be at 1050
to figure out,
1000(1.05)
1050(1.05)
.......
until you get to 2000, each step is a year...

Answer 9

F=A
F+A=2A

A.n.5/100=A

5n=100
n=20 years