Please explain and break down simply how the math was done to find the present value in the explanation. Thank you

1. You want to borrow 10000. Bank A offers you a loan contract according to which you have to pay back the loan in 10 annual installments of 1200 per year (the first installment is due one year after signing the contract). Bank B also offers you a contract with 10 annual installments, but you have to pay 1100 annually during the first 5 years and 1300 annually during years 6 - 10. Finally, bank C requires you to pay annually 1300 during years 15 and 1100 during years 610. Which of the three contracts is best for you if you want to miminize the present value of the installments based on a constant annual interest rate of 5% ? Loan amount =10000 Constant Annual interest rate of 5% Options:: Bank A:: Payback loan at 1200 p.a. For 10 instal ments. Present Value @5\% for 10years 7.7182 PV=7.71821200 PV=9262 Bank. B :: First 5 years-- 1100 Next 5 years -- 1300 PV=11004.3284 +13003.3899 =4761+4407 =9168 PV=9168 Explanation: Bank C: : First 5years-- 1300 Next 5 years 1100 PV=13004.3284 +11003.3899 PV=5627+3729 PV=9356