Anna borrows $ 1.5 million to buy an apartment. the annual interest rate for the loan is 3%. Anna will repay the loan in ten years with ten equal annuities.

(a) Anna divides the annuities and pays one twelfth of the annuity each month. How much should Anna pay to the bank each month? The value of the ten annuities together shall be equal to the value of the entire loan amount with ten years' interest. Use the formula for the sum of a geometric sequence of numbers and plot an equation from which you can solve the annuity.

(b) How many years would it take to repay the loan if Anna wanted to pay exactly $ 5,000 a month? Set up and solve the corresponding equation as in problem (a), but this time you must solve the equation with respect to the number of years. Remember that the number of years will be included in both the left and the right.