3. How long, to the nearest tenth of a year, will it take $12,500 to grow to $20,000 at 6.5% annual interest compounded quarterly? (Use the formula for compound interest with n compoundings per year to solve for t.)
A = final amount = 20000
P = beginning amount = 12500
r = annual interest rate expressed as a decimal = .065
n = number of times a year the interest is compounded = 4 (quarterly)
t = number of years it takes P to grow to A = what we want to find
Take the log of both sides:
Use this rule of logs:
Subtract from both sides:
Divide both sides by
Cancel:
Now substitute
A = final amount = 20000
P = beginning amount = 12500
r = annual interest rate expressed as a decimal = .065
n = number of times a year the interest is compounded = 4 (quarterly)
That's over 7 years. To find out how many months, multiply the
fractional part .289417683 by 12, getting 3.473012194
So 7 years 3 months the amount will be less than $20000 and 7 years
4 months it will be more than $20000.
Edwin