(a) A bank offers a savings account with an AER of 10% compounded monthly. If a customer saves 110 euros per month starting now, how much will the customer have in five years' time?
(b) A loan for €450,000 is taken out at an APR of 5.2%. How much should annual repayments be if the loan is to be repaid in 15 equal installments over a 15-year period? Assume the first installment is paid at the end of the first month.
(c) A couple agrees to take out a mortgage of €450,000 at a rate of 0.3% per month, in order to purchase a new home. This loan is to be paid back monthly over 25 years with repayments due at the end of each month. The amount of each repayment is €1771. After exactly 11 years of repayments, the couple receives a windfall and decides to repay the remaining balance on the mortgage. Write down a series including the first and last two terms which shows the total of the present values of all the remaining 14 years of the mortgage (after the last monthly repayment at the end of year 11). Hence find how much the couple will need to repay in order to clear their mortgage entirely. Give your answer correct to the nearest cent.