if 2500 is invested at an interest rate of 6.5% compounded monthly how long will it take for the investment to reach 7500

To find the time it will take for the investment to reach $7500, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($7500 in this case)
P = the principal amount (initial investment of $2500)
r = the annual interest rate (6.5%)
n = the number of times interest is compounded per year (12 for monthly compounding)
t = the time in years

We need to solve for t in this case, so let's rearrange the formula:

A/P = (1 + r/n)^(nt)

7500/2500 = (1 + 0.065/12)^(12t)

3 = (1 + 0.0054167)^(12t)

To solve for t, we can take the natural logarithm (ln) of both sides and isolate t:

ln(3) = ln(1.0054167)^(12t)

ln(3) = 12t * ln(1.0054167)

t = ln(3) / (12 * ln(1.0054167))

By plugging in these values into a calculator, we can find the approximate value of t.

i = .065/12 = .0054166...

2500(1.0054166..)^n = 7500 , where n is the number of months
1.0054166..^n = 3
log both sides, and use log rules

n log 1.0054166.. = log3
n = aprr 203.37 months
= 16.95 years