Question

Studies show that the average American has $4,878 in credit card debt with an average interest rate of 12.78% compounded monthly. If it took the average American 20 years to pay off their debt, how much would they be paying total?

Formula to use: y = a * b^x (or a = p(1+r/n)^nt)

Answer 1

They would be paying a total of $62,005.34¢

Explanation:

In order to calculate the total amount that an average American who borrowed the sum will pay, we will be making use of the compound interest formula since the interest on the loan given to an average American is compounded monthly.

Formula for compound interest is:

Fv = Pv × (1 + r/n)^n×t

Where,

Fv = future value (the total amount that an American will pay)

Pv = present value (initial amount borrowed)

r = rate of interest

n = number of times of compounding in a year

t = time (period a loan will run)

Here,

Pv = 4,878

r = 12.78% or 0.1278

n = 12(every month)

t = 20

Substituting appropriately we will have:

Fv = 4,878 × [1 + (0.1278/12)]^12×20

= 4,878 × (1 + 0.01065)^240

= 4,878 × (1.01065)^240

= 4,878 × 12.7112213

= $62,005.34¢

Therefore, the total amount that an American who borrowed that initial amount will be paying after a period of 20 years is $62,005.34¢

Answer 2

$62,005.34

Explanation:

If the interest rate is 12.78% compounded monthly, we can use the formula a = p(1+r/n)^nt

where a is the final value to be paid, p is the inicial value, r is the interest rate, n is the number of months in a year and t is the time in years

So, the total debt will be:

y = 4878 * (1+0.1278/12)^240 = $62,005.34