Question

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

Answer 1

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

Answer 2

\[890.2=400e^{16r}\] solve for r

Answer 3

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

Answer 4

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

Answer 5

@krishna, it is compounded "continuously"

Answer 6

oh yes, my mistake.

Answer 7

thought it was just compound

Answer 8

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

Answer 9

i made a mistake, it should be
\[2.2255\]

Answer 10

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