Find the present value of the following cash flows:

$(1)$ A fifteen year annuity of $$300$ starting at T$3.$ Interest rates are $6\%.$

$(2)$ A seven year annuity of $$450$ starting in five year's time. Interest

rates are $11\%$

$(3)$ A perpetuity of $$33,000$ commencing at T$2.$ Interest rates are $22\%$

$(4)$ A perpetuity of $$14,000$ starting in ten year's time. Interest rates are $12\mathrm{.}5\%$

$(5)$ A perpetuity of $$2,000$ starting in six year's time, growing at $3\%$ per annum. Interest rates are $10\%$

Please help me calculation this without using chatgpt