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.
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
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