Question

Robert is repaying a debt with 18 annual payments of 1200 dollars each, the first coming a year from now. At the end of the 4th year, he makes an extra payment of 2400 dollars. He then shortens his remaining payment period by 2 years, and makes level payments over the remaining time. If the effective rate of interest is 8.3 percent, how large is his new annual payment?

Answer 1

Calculating Value of Debt with Fixed payment of $1,200

Using TVM Calculation,

PV = [FV = 0, PMT = -1,200, N = 18, I = 0.083]

PV = $11,016

Calculating Value of Loan at the end of Year 4,

Using TVM Calculation,

FV = [PV = 11,016, PMT = -1,200, N = 4, I = 0.083]

FV = $9,723

With $2,400 payment,

Amount remaining = 9,723 - 2,400 = $7,323

Time Period = 12 years

Calculating Annual Payment,

Using TVM calculation,

PMT = [PV = 7,323, FV = 0, N = 12, I = 0.083]

PMT = $986.88

Annual Payment = $986.88