I already posted this question,and Henrey answered it. I just wanted to clarify a few things to make sure I am on the right track
Problem: Joanie takes a $6,000 loan to pay for her car. The annual interest reate 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? Express your answer as a dollar value to the nearest cent.
•Math - Henry, Friday, November 21, 2014 at 7:22pm:
P1 = Po*(1+r)^n. Compounded annually.
r = 12%/100% = 0.12 = Annual % rate expressed as a decimal.
n = 1Comp./yr. * 4yrs. = 4 Compounding
periods.
P1 = 6,000*(1.12)^4 = $9441.12
P2 = Po*(1+r)^n. Compounded quarterly.
r = (12%/4)/100% = 0.03 = Quarterly %
rate.
n = 4Comp./yr. * 4yrs. = 16 Compounding
periods.
Plug the above values into the given Eq
and solve for P2.
P2-P1 =
Now do I just plug in $9441.12 into P2 = Po*(1+r)^n? Please help!
No, do P2 now
P2 = 6,000 (1.03)^16
then find P2 -P1
amount owing at 12% compounded annually in 4 years
= 6000(1.12)^4 = 9441.12
amount owing at 12% per annum compounded quarterly in 4 years
= 6000(1.03)^16 = 9628.24
Now subtract them as Henry told you to do.
To calculate the amount she will owe if the interest compounds quarterly (P2), you need to use the formula P2 = Po*(1+r)^n. In this case, Po represents the initial loan amount of $6,000, r represents the quarterly interest rate which is equal to (12%/4)/100% = 0.03, and n represents the number of compounding periods which is equal to 4 compounding periods per year multiplied by 4 years, yielding 16 compounding periods.
So to calculate P2, you would need to plug in these values into the formula:
P2 = 6,000*(1+0.03)^16 = $9,874.83
To find out how much more money she will owe if the interest compounds quarterly than if it compounds annually, you subtract the amount owed with annual compounding (P1) from the amount owed with quarterly compounding (P2):
P2 - P1 = $9,874.83 - $9,441.12 = $433.71
Therefore, Joanie will owe approximately $433.71 more if the interest compounds quarterly compared to if it compounds annually.