# A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college ch?

A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college charges \$2,100 to pay for college expenses, and intends to pay it in one year, what will she have to pay? (Round your answer to the nearest cent.)

Relevance

So you borrow \$2100 at the beginning of year and intend to pay it all back along with interest at the end of year.

nominal interest rate = i = 22%

n = number of periods = 12

The effective interest rate = r = (1+i/n)^n - 1 = (1 + 0.22/12)^12 - 1 = 0.2436 or 24.36%

payment = \$2100 * (1+r) = \$2611.56

• L = loan amount = 2100

i = 22% = 0.22

P = payment

L = P/(1 + i/12) + P / (1 + i/12)^2 + ... + P / (1 + i/12)^12

L = P * sum((1 + i/12)^(-t) , t = 1 , t = 12)

Let 1/(1 + i/12) = r

L = P * sum(r^t , t = 1 , t = 12)

S = r + r^2 + r^3 + ... + r^12

S * r = r^2 + r^3 + ... + r^12 + r^13

Sr - S = r^13 - r

S * (r - 1) = r * (r^12 - 1)

S * (1 - r) = r * (1 - r^12)

S = r * (1 - r^12) / (1 - r)

L = P * r * (1 - r^12) / (1 - r)

L * (1 - r) / (r * (1 - r^12)) = P

r = 1 / (1 + i/12)

r = 1 / ((12 + i) / 12)

r = 12 / (12 + i)

r = 12 / (12 + 0.22)

r = 12 / (12.22)

L * (1 - (12 / 12.22)) / ((12 / 12.22) * (1 - (12/12.22)^12)) = P

P = 2100 * ((12.22 - 12) / 12.22) / ((12 / 12.22) * ((12.22^12 - 12^12) / 12.22^12))

P = 2100 * (0.22) * 12.22^12 / (12 * (12.22^12 - 12^12))

P = 2100 * 0.09359437964208574225766219148281

P = 196.5481972483800587410906021139

\$196.55 a month

• For Credit and finance solutions I recommend this website where you can find all the solutions. http://LOANSANDFINANCES.INFO/index.html?src=5YAPZP...

RE :A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college ch?

A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college charges \$2,100 to pay for college expenses, and intends to pay it in one year, what will she have to pay? (Round your answer to the nearest cent.)