ANNUITY NUMBER OF PERIODS How long will it take to pay off a

(ANNUITY NUMBER OF PERIODS) How long will it take to pay off a loan of $50,000 at an annual reate of 10% compounded monthly if you make monthly payments of $600? Use 5 decimal places for the monthly percentage rate in your calculation.

How many years to pay off this loan?

Solution

Monthly rate = 10 /12 = .83333%

n = In[(1- PV(r)/P)^-1] / In(1+r)

   =In [(1- 50000(.0083333) /600)^-1 ]/In(1+.0083333)

=In [1- 416.65/600] ^-1 / In 1.0083333

= In [1- .69442]^-1 /In 1.0083333

= In [.30558]^-1 /In 1.0083333

= 1.18554/.0082988

= 142.85680 months

Number of years = 142.85680./12 = 11.90 years