An 11-year annuity has a series of payments 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, with the first payment made at the end of the second year. The present value of this annuity is 25 at interest rate i i. A twelve-year annuity has a series of payments 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, with the first payment made at the end of the first year. Calculate the present value of the 12-year annuity at interest rate i i.

Secured loans are protected by collateral security. examples: title loans where the borrower uses the car title as collateral security interest rates are lower and repayments are longer therefore risk is low as a collateral security is given as guarantee to the bank in case of failure to pay the loanunsecured loans are not protected by collateral security but it is given on the creditworthiness of the borrower, trusting that she/he will pay on time. examples; payday loans is a short term loan where the borrower lends money from the bank and pays is back when the borrower receives his/her wages.interest rates are high and repayments are shorter. but the risk is high as no collateral security is given as a guarantee to the bank for payment of the loan

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