Tommy owes 3000 on his credit card. He is paying 14.5% interest compounded monthly. If it takes him 4 years to pay off the balance, what was the total amount that he ended up paying.
Okay, so it gives me the equation a=p(1+r/n)^nt
I did 3000(1+.145/12)^48 and got $5339.52
Is this correct?
This is the formula for compound interest on a fixed deposit.
It is not the formula for loan amortization, which takes into account the declining balance.
Better check you formula list.
However, if that's the formula you were supposed to use, you did it right.
It is the formula my teacher gave me so I suppose that's what I'm supposed to do. Thank you.
Yes, your calculation is correct.
To explain in detail, let's break down the formula you used:
a = p(1 + r/n)^(nt)
where:
a = total amount paid
p = principal amount (initial debt) = $3000
r = annual interest rate in decimal form = 14.5% = 0.145
n = number of times interest is compounded per year = 12 (since it's compounded monthly)
t = time in years = 4
Plugging these values into the formula, we get:
a = 3000(1 + 0.145/12)^(12*4)
= 3000(1 + 0.01208333333)^(48)
= 3000(1.01208333333)^(48)
≈ $5339.52 (rounded to two decimal places)
So, the total amount Tommy ended up paying is approximately $5339.52.