Question

Financial Math: A loan of $20,000 at an annual effective interest rate of 5% is to be repaid by annual end-of-year payments of $6000. Find the total length of the loan and the amount of the final payment if (1) the final payment is paid during the year following the last regular payment. (Answer: 3.7369 years, $4,392.91) (2) the final payment is a balloon payment. (Answer: 3 years, $10,237.50) (3) the final payment is a drop payment. (Answer: 4 years, $4,449.38) Please show work

Answer 1

Loan Amount = $20,000

Interest Rate = 5%

Annual Payment = $6,000

Calculating Time Period when remaining loan balance is smaller than $6,000

T = [PV = 20,000, FV = 0, PMT = -$6,000, I = 0.05]

T = 3.7369

But,

Last Regular Payment is Balloon Payment so Last Payment is Year 3,

Calculating Balloon Payment(Calculating Remaining Loan at the end of Year 3)

FV = [PV = 20,000, T = 3, PMT = -$6,000, I = 0.05]

FV = $4,237.5

So,

Balloon Payment = Regular Payment + 4237.5

Balloon Payment = 6000 + 4237.5

Balloon Payment = $10,237.50

So,

Term of Loan is 3 years and Balloon Payment is $10,237.50