Jason has $3,491.15 in credit card debt. The annual interest rate on the unpaid balance is 19.4% compounded monthly. If Jason wants to pay off his credit card debt in 2 years, what is his monthly payment, assuming he makes no additional purchases on this card? (Suggestion: Use the formula for the present value of an ordinary annuity. Round your answer to the nearest cent.) show your work
To calculate Jason's monthly payment, we can use the present value formula for an ordinary annuity:
\[PV = Pmt \times \left(1 - \frac{1}{(1+r)^n}\right) \div r\]
Where:
- PV = present value of the debt ($3,491.15)
- Pmt = monthly payment we need to find
- r = monthly interest rate (19.4%/12 = 0.0194/12 = 0.0162)
- n = number of payments (2 years * 12 months = 24)
Substitute the values into the formula:
\[3491.15 = Pmt \times \left(1 - \frac{1}{(1+0.0162)^{24}}\right) \div 0.0162\]
\[3491.15 = Pmt \times \left(1 - \frac{1}{(1.0162)^{24}}\right) \div 0.0162\]
\[3491.15 = Pmt \times \left(1 - \frac{1}{1.42571260655}\right) \div 0.0162\]
\[3491.15 = Pmt \times \left(1 - 0.70016346691\right) \div 0.0162\]
\[3491.15 = Pmt \times 0.29983653309 \div 0.0162\]
\[3491.15 = Pmt \times 18.534375\]
\[Pmt = 3491.15 / 18.534375\]
\[Pmt ≈ 188.45\]
Therefore, Jason's monthly payment to pay off his credit card debt in 2 years would be approximately $188.45.