Joanie takes a $6000 loan to pay for her car. The interest rate on the loan is 12%. She makes no payments for 4 years, but has to pay back all the money she owes at the end of 4 years. How much more money will she owe if the interest compounds quarterly than if the interest compounds annually?
I already figured out that if the interest compounds annually, she will pay $9441.12. The equation I used for that was:
(1.12)^4 (6000)
I am having trouble finding the equation that is similar to the one I showed above to figure out what would happen if the interest compounds quarterly. Please help if you can!
Thank you! :-)
the quarterly interest rate would be 12%/4 = 3%
but there are 16 quarters in 4 years.
so the amount would be 6000(1.03)^16 = 9628.24
which is $187.12 more than had it been compounded annually.
To find out how much more money Joanie will owe if the interest compounds quarterly instead of annually, you can use the formula for compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (total owed)
P = the principal amount (initial loan amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $6000, the annual interest rate (r) is 12% or 0.12, the number of times interest is compounded per year (n) is 1 (for annually), and the number of years (t) is 4.
To calculate the amount Joanie will owe if the interest compounds quarterly, you will need to adjust the values in the formula. Since interest compounds quarterly, the number of times interest is compounded per year (n) will be 4 (quarterly).
Using the formula with the adjusted values:
A = 6000(1 + 0.12/4)^(4*4)
A = 6000(1 + 0.03)^16
A = 6000(1.03)^16
Calculating this expression will give you the amount Joanie will owe if the interest compounds quarterly.