Question

Cal Lury owes $23,000 now. A lender will carry the debt for seven more years at 8 percent interest. That is, in this particular case, the amount owed will go up by 8 percent per year for seven years. The lender then will require that Cal pay off the loan over the next 15 years at 11 percent interest.

  
What will his annual payment be?

Answer 1

Present value (PV) of debt = $23,000

Number of years (n) = 7 years

Rate of interest (i) = 8%

Compute Future value,

FV =  PV * ( 1 + i )ⁿ

= 23000 (1 + 0.08)⁷

= 23000 * 1.71382

= 39417.95818

ie, the value of his debt after 7 years will be $39417.95.

Computation of annual payments

Rate of interest = 11%

Number of years = 15 years

Annual payments = 39417.95818 / Annuity present value factor at 11% for 15 periods

= 39417.95818 / 7.19086

= 5481.667854

Therefore his annual payments will be $5481.667

working note

The formula for computing annuity PV factor = [ 1 - (1 + i )^-n ] / i

= [ 1 - (1 + 0.11 )^-15 ] / 0.11

= [ 1 - (1.11 )^-15 ] / 0.11

= [ 1 - 0.209004 ] / 0.11

= 0.79099 / 0.11

= 7.19086