A value grows exponentially each year, the value after four years and ten years has grown to 2385 and 3106. The percentage value grows each year? ??

Question

kropot72 · Answer

2385 = A(1 + r)^4
3106 = A(1 + r)^10
Where A is the original amount, r is the annual interest rate and the exponents are the number of years
Taking logs of both sides of the above equations gives:
$$\ln 2385=\ln A + 4\ln (1+r).............(1)$$
$$\ln 3106=\ln A+10\ln (1+r).............(2)$$
Subtracting (1) from (2) gives:
$$\ln 3106-\ln 2385=6\ln (1+r)$$
From which we get$$\ln (1+r)=0.44$$
Can you now solve for r?

kropot72 · Answer

$$\ln (1+r)=0.44$$
Therefore$$1+r=e ^{0.44}=1.045$$
$$r=1.045-1=?$$

anonymous · Answer

r = 0,045? is that the % ? , why 1+r=e0.44 ? dont understand where the e comes from?

kropot72 · Answer

The exponential number e is the base of natural logarithms. The percentage rate is 0.045 * 100 = 4.5%

anonymous · Answer

Thanks :) I always have to use e when i use Ln ?

kropot72 · Answer

You're welcome :)
 From the basic laws of logarithms, if$$e ^{a}=b$$
then$$\ln b=a$$