After how many years is a $100 investment worth twice as much at 7% per annum then at 4.5% per annum
+130516 We have
M = 100(1.045)^t
And we are trying to find
2M = 100(1.07)^t
So we have.....substituting the first equation into the second
2(100)(1.045)^t = 100(1.07)^t
2(1.045)^t = 1.07^t
2 = (1.07)^t / (1.045)^t
2 = (1.07/1.045)^t take the log of both sides
log2 = log (1.07/1.045)^t so
t = log2 / log(1.07/1.045) = about 29.318 years
Proof
100(1.045)^29.318 = $363.45
100(1.07)^29.318 = $726.89
And the second amount is roughly twice as much as the first.
+130516 We have
M = 100(1.045)^t
And we are trying to find
2M = 100(1.07)^t
So we have.....substituting the first equation into the second
2(100)(1.045)^t = 100(1.07)^t
2(1.045)^t = 1.07^t
2 = (1.07)^t / (1.045)^t
2 = (1.07/1.045)^t take the log of both sides
log2 = log (1.07/1.045)^t so
t = log2 / log(1.07/1.045) = about 29.318 years
Proof
100(1.045)^29.318 = $363.45
100(1.07)^29.318 = $726.89
And the second amount is roughly twice as much as the first.
