Cal Lury owes $25,000 now. A lender will carry the debt for four more years at 1
ID: 2739882 • Letter: C
Question
Cal Lury owes $25,000 now. A lender will carry the debt for four more years at 10 percent interest. That is, in this particular case, the amount owed will go up by 10 percent per year for four years. The lender then will require that Cal pay off the loan over the next 12 years at 13 percent interest.
What will his annual payment be? Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
What will his annual payment be? Use Appendix A and Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation / Answer
The loan amount in four years will be the future value of $25000 at the and of four years from now compounded at 10% p.a.
= 25000*fvif(10,4) = 25000*1.4641 = $36602.5
This amount of 36602.5 is the PV of the annuity (equal annual payments against interest and principal).
So 36602.5 = Annuity * pvifa(13,12) = A*5.9176
A = 36602.5/5.9176 = $6,185.36
Using the formulae it will be:
Loan amount at the end of four years = 25000*1.1^4 = 36602.5
Annuity = (36602.5*0.13*1.13^12)/(1.13^12 - 1) = $6185.31
Difference is very insignificant and is due to rounding off in finding interest factors (first method)