Question

How long will it take an investment of $8000 to double if the investment earns interest at the rate of 6%/year compounded monthly? (Round your answer to one decimal place.) 11.6 Correct: Your answer is correct. yr

Answer 1

11.58 years

Step-by-step explanation:

Data provided in the question:

The value of the Amount invested = $8,000

Interest rate on the investment = 6% per year

Monthly interest rate =
`(6\%)/(12)` = 0.5% per month = 0.005

Future value = 2 × $8,000 = $16,000

Now,

using the compound interest formula

Future value = Present value × (1 + r)ⁿ

Here,

r is the interest rate

n is the number of months

thus,

$16,000 = $8,000 × (1 + 0.005 )ⁿ

or

2 = 1.005ⁿ

now,

on taking the log both sides, we get

log(2) = log(1.005ⁿ)

now using the property of log

log(aᵇ) = b × log(a)

thus,

log(2) = n × log(1.005)

or

0.30103 = n × 0.002166

or

n = 138.97 ≈ 139 months

or

n =
`(139)/(12)`

or

n = 11.58 years