Problem 1. Jana, who just turned 55, would like to have an annual annuity of $25,000 paid each year for 15 years, the first payment occurring on her 66th birthday. How much must Jana save each year (at the end of the year) for the next 10 years to have this annuity, if the interest rate is 8%?
Problem 2. You are considering a 30 year mortgage of $150,000 at 6% compounded monthly.
a) Find the payment amount on the mortgage.
b) Closing costs are 3% of the mortgage amount, are paid up front (when the loan is made) and are deducted from the loan proceeds. Find the APR on the mortgage (include the closing costs in determining the APR).
c) Suppose that in 10 years (after the 120th payment) interest rates fall. At what interest rate is it wise (you save money) to refinance the loan for a 20 year term? You will pay closing costs of 3% of the amount refinanced up front. Assume money is worth 7.2% compounded monthly (to you).