BEEF asked in Science & MathematicsMathematics · 9 years ago

# 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
• 9 years ago

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

• 9 years ago

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

• Bevvy
Lv 6
3 years ago

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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.)