Question 1188721
7% annual interest compounded quarterly is equal to (7/4)% per quarter.


(7/4)% = 1.7% each quarter.


divide that by 100 to get a rate of .0175 and add 1 to it to get a growth rate of 1.0175 per quarter.


you want to know how long before your money reaches 12400.


1.55 = 1.0175 ^ x, where x represents the number of quarters.


take the log of both sides of this equation to get:


log(1.55) = log(1.0175 ^ x).


since log(1.0175 ^ x) is equal to x * log(1.0175), this becomes:


log(1.55) = x * log(1.0175).


divide both sides of the equation by log(1.0175) to get:


log(1.55) / log(1.0175) = x


solve for x to get:


x = 25.26163279.


that's how many quarters of a year it will take.


divide that by 4 to get:


x = 6.315408196 years.



confirm by solving for y = 8000 * 1.0175 ^ 25.26163279 to get:


y = 12400.


the equation that i worked from is:


f = p * (1 + r) ^ n


f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.


you were given the rate per year of 7%.
divide that by 100 to get .07 per year.
divide that by 4 to get .0175 per quarter.


your time periods are in quarters of a year.


the equation became:


12400 = 8000 * (1 + .0175) ^ n


divide both sides of the equation by 8000 to get:


12400 / 8000 = (1 + .0175) ^ n


take the log of both sides of the equation to get:


log(12400 / 8000) = log((1 + .0175) ^ n) which becomes:


log(12400 / 8000) = n * log(1 + .0175).


divide both sides fo log(1 + .0175) to get:


log(12400 / 8000) / log(1 + .0175) = n


solve for n to get:


n = 25.26163279.


sine the time periods were in quarters of a year, then the solution is 25.26163279 quarters of a year, which, when divided by 4, gives you the number of years.