Mathmatics of investment and credit.

Please GIVE CLEARLY FORMULA and answer ALL the questions.

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1. Consider a 96-payment annuity, where each payment is $50. (a) Suppose that the effective periodic interest rate is 0.75%. Find: i, the present value of the annuity one period before the first payment; ii. the present value of the annuity at the time of the first payment; iii. the accumulated value of the annuity at the time of the last payment; iv. the accumulated value of the annuity one period after the last payment; V. Express the relationships between the quantities you found in ()-(iv) using the interest rate (or the present value factor). [HintRecall the relationships between ni, Ani, SniSni.] (b) Suppose that the effective periodic interest rate is 0.75% until the 33rd payment, and then it changes to 1%. Find : i , the present value of the annuity one period before the first payment; ii. the present value of the annuity at the time of the first payment; iii. the accumulated value of the annuity at the time of the last payment; iv. the accumulated value of the annuity one period after the last payment; V. Express the relationship between the quantities you found in (-(iv) using the interest rates (or the present value factors)