Question 171285: If $1500 is deposited in a savings account paying 5% compounded quarterly, how long will take the account to increase to $2000? Found 2 solutions by midwood_trail, gonzo:Answer by midwood_trail(310) (Show Source):
You can put this solution on YOUR website! If $1500 is deposited in a savings account paying 5% compounded quarterly, how long will take the account to increase to $2000?
Use the following formula:
Compound Quarterly = P (1 + r/4)^4
P is the principal (the initial amount you borrow or deposit)
r is the annual rate of interest (percentage)
n is the number of years the amount is deposited or borrowed for.
A is the amount of money accumulated after n years, including interest.
You can put this solution on YOUR website! let PV be present value of the investment.
let FV be future value of the investment.
let i be the interest rate
let n be the number of time periods.
standard equation to solve this is:
-----
PV = 1500
FV = 2000
annual interest rate = 5% / 100% = .05
quarterly interest rate = annual interest rate / 4 = .05 / 4 = .0125
1 + .0125 = 1.0125
your number of time periods is n which will be in quarters of a year.
you need to solve for number of time periods.
-----
your equation to solve is:
2000 = (1500)*(1.0125)^n
divide both sides of equation by 1500:
1.0125^n = 2000/1500
you should be able to use logarithms to solve this: if and only if
in order to solve this using a calculator, you need to convert the base to either 10 or e, whichever the calculator handles.
we'll use the base of 10 which is the log function on the calculator.
the general form of the base conversion formula is:
-----
in your logarithmic equation,
a = 1.0125
x = (2000/1500)
your logarithmic equation becomes:
-----
to prove this is correct, use your calculator and take and you'll see that the answer comes out to be 1.3333333333333 which is the same as 2000/1500.
-----
it will take 23.15810902 quarters to reach 2000.
divide that by 4, and it will take 5.789527255 years.
-----
the investment is made at the beginning of each time period.
the time periods are quarters of a year (4 time periods per year).
the division of the annual rate by 4 to get a quarterly rate is the industry standard way to do this. if you were compounding monthly, you would take the annual interest rate and divide by 12. the number of periods, in that case, would be 12 periods per year.
-----
(
