Pls answer 3rd and 4th

Functions 1. Consider a loan of $60 000, which is to be repaid in 120 monthly instalments starting one month after the loan has been taken out. The interest on the loan is 5% per year compounded monthly. (a) Find the size of the regular repayments. (b) What are the Interest and Principal parts of the 50th repayment? (Note that you should not be using a table with 50 payments! You must use the formulas which were used in lectures). 2. An annual prize is to be established for the best student in Introduction to Financial Mathematics (not really). The prize money comes from a perpetuity paying interest of 3% per year compounded quarterly. The prize will pay a fixed amount each year, starting in one year's time. If the initial deposit is $36 000, how much is the prize worth? Algebra 3. Formulate the following problem as a linear program in standard form. A manufacturer of oil paints, for artists, needs three different pigments, A, B and C to mix three different shades of red paint. The three shades of paint are: Scarlett, Ruby, and Maroon. The manufacturer has 50 kg of type A pigment, 60 kg of type B pigment, and 30 kg of type C pigment. The amounts of pigment in unit of 1 kg/ litre needed for each shade are given in the following table. Ruby Maroon Pigment Shade Scarlett A 2 B 1 2 0 2 The objective is to maximise the volume of paint, given the holdings of pigments. 4. Given the holdings of pigment, maximise the number of litres of paint the manufacturer can place under crop using the Simplex algorithm. Functions 1. Consider a loan of $60 000, which is to be repaid in 120 monthly instalments starting one month after the loan has been taken out. The interest on the loan is 5% per year compounded monthly. (a) Find the size of the regular repayments. (b) What are the Interest and Principal parts of the 50th repayment? (Note that you should not be using a table with 50 payments! You must use the formulas which were used in lectures). 2. An annual prize is to be established for the best student in Introduction to Financial Mathematics (not really). The prize money comes from a perpetuity paying interest of 3% per year compounded quarterly. The prize will pay a fixed amount each year, starting in one year's time. If the initial deposit is $36 000, how much is the prize worth? Algebra 3. Formulate the following problem as a linear program in standard form. A manufacturer of oil paints, for artists, needs three different pigments, A, B and C to mix three different shades of red paint. The three shades of paint are: Scarlett, Ruby, and Maroon. The manufacturer has 50 kg of type A pigment, 60 kg of type B pigment, and 30 kg of type C pigment. The amounts of pigment in unit of 1 kg/ litre needed for each shade are given in the following table. Ruby Maroon Pigment Shade Scarlett A 2 B 1 2 0 2 The objective is to maximise the volume of paint, given the holdings of pigments. 4. Given the holdings of pigment, maximise the number of litres of paint the manufacturer can place under crop using the Simplex algorithm