An investment of $400 increased to $890.20 in 16 years. If interest was compounded continuously, find the interest rate.

Question

anonymous · Answer

the formula is Investment * (1 + interest)^years  = end amount

anonymous · Answer

$$890.2=400e^{16r}$$ solve for r

anonymous · Answer

1) divide by 400
2) take the log
3) divide by 16

anonymous · Answer

so substitute the values to get 400 * (1 + x)^16 = 890.2
and solve for x to get x = 10.04 % interest

anonymous · Answer

@krishna, it is compounded "continuously"

anonymous · Answer

oh yes, my mistake.

anonymous · Answer

thought it was just compound

anonymous · Answer

$$2.225=e^{16r}$$
$$\ln(2.225)=16r$$
$$r=\frac{\ln(2.225)}{16}$$ then a calculator

anonymous · Answer

i made a mistake, it should be 
$$2.2255$$

anonymous · Answer

so answer is 
$$r=\frac{\ln(2.2255)}{16}$$