Question

If you deposit $5000 into an account paying 6% annual interest compounded monthly, how long until

there is $8000 in the account?

Answer 1

7.85 years which I think rounds to about 7 years and 11 months

Explanation:

The formula for compound interest is

`AV=PV*(1+(i)/(n))^(t*n)`

Where AV = Accumulated Value (or Future value)

PV= Present value

i= nominal interest rate

n= number of times compunded in a period (here a period is a year)

t= number of periods (years in this case)

We can plug this numbers in to get

8000=5000*(1+(.06/12))^12x

First we divide by 5000 to get

1.6=(1.005)^12x

We can rewrite this into a logarithim

log₁.₀₀₅1.6=12x

The formatting here is kind of weird but I'm trying to say that log base 1.005 1.6 = 12x

We can compute this and get

94.2355=12x

divide by 12 to get that

x=7.85 Years