Thor invests some money in an account earning 8% interest, compounded continuously. After how many years will he double his investment? [Use the formla A = Pert and round answer to the nearest tenth.]
A) 6.2 years
B) 7.5 years
C) 8.7 years
D) 9.9 years
"I think the answer is B"
Po*e^(rt) = 2Po.
Divide both sides by Po:
e^rt = 2.
rt = 0.08t.
e^0.08t = 2.
0.08t*Log e = Log 2.
0.08t = Log2/Log e = 0.693
t = 8.7 yrs.
To find out how many years it will take for Thor to double his investment, we can use the formula for continuous compound interest:
A = Pert
Where:
A = final amount (double the initial amount)
P = initial principal (Thor's investment)
e = base of natural logarithms (approximately 2.71828)
r = annual interest rate (8% or 0.08)
t = time in years (what we need to find)
We can rearrange the formula to solve for t:
t = ln(A/P) / r
Since we want to find the number of years it takes for Thor's investment to double, we plug in the following values into the formula:
A = 2P (double the initial investment)
r = 0.08 (8% as a decimal)
t = ln(2P/P) / 0.08
Simplifying further, we have:
t = ln(2) / 0.08
Using a calculator, the value of ln(2) is approximately 0.6931. Plugging it into the formula:
t = 0.6931 / 0.08
t ≈ 8.7 years (rounded to the nearest tenth)
So the correct answer is C) 8.7 years.