Tae takes out a loan for $5000,to be paid back with monthly payments of $199 for as long as is needed.The first payment of $199 is due exactly 6-months after the loan is taken out.Tae also plans to increase the size of the final payment (that is,he plans to make a balloon payment,not a drop payment).If the interest rate on the loan is j₁₂ = 12%,how many payments are needed?

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity (PV = PMT/(r/12)*(1 - (1+r/12)^(-n))), we can solve for the number of payments needed. Plugging in the given values, we get:

5000 = 199/(0.01)*((1 - (1+0.01)^(-n))

Solving for n (using a calculator or trial and error), we find that n is approximately equal to 30. Therefore, Tae will need to make 30 monthly payments of $199, plus a final balloon payment to fully repay the loan.

Tae Takes Out a Loan for $5000,to Be Paid Back