Theory of Interest Problem: I KNOW THE ANSWERS I NEED HELP WITH THE WORK. PLEASE ATTACH YOUR WORK FOR ANY OF THESE PROBLEMS IF IT MATCHES THE ANSWER. ANSWER FOR #1. 220+ln(23/3), #2. (a) 276; (b) 269; (c) 564976.30; (d) 255472.73

1. [1.5 pts] A continuous varying annuity is payable for 20 years, starting at t = 2. The rate of payment at time t is t2per year. Suppose the force of interest at time t is t= 1/(t + 1) for t 0. Find the present value of the annuity at t = 0. 2. [2 pts] A house is purchased for $350,450. A down payment of 15% is made and the remainder is financed with a thirty-year fixed loan to be paid off in monthly installments at the end of each month. Assume the annual interest rate is 9% convertible monthly. a) At what time does the balance reach 50% of the amount originally financed? b) At what time does the percentage of each payment to principal first exceed 50%? c) What is the total amount of interest paid? d) What is the loan balance just after payment number 145?

1. [1.5 pts] A continuous varying annuity is payable for 20 years, starting at t=2. The rate of payment at time t is t2 per year. Suppose the force of interest at time t is t=1/(t+1) for t0. Find the present value of the annuity at t=0. 2. [2 pts] A house is purchased for $350,450. A down payment of 15% is made and the remainder is financed with a thirty-year fixed loan to be paid off in monthly installments at the end of each month. Assume the annual interest rate is 9% convertible monthly. a) At what time does the balance reach 50% of the amount originally financed? b) At what time does the percentage of each payment to principal first exceed 50% ? c) What is the total amount of interest paid? d) What is the loan balance just after payment number 145 ? 1. [1.5 pts] A continuous varying annuity is payable for 20 years, starting at t=2. The rate of payment at time t is t2 per year. Suppose the force of interest at time t is t=1/(t+1) for t0. Find the present value of the annuity at t=0. 2. [2 pts] A house is purchased for $350,450. A down payment of 15% is made and the remainder is financed with a thirty-year fixed loan to be paid off in monthly installments at the end of each month. Assume the annual interest rate is 9% convertible monthly. a) At what time does the balance reach 50% of the amount originally financed? b) At what time does the percentage of each payment to principal first exceed 50% ? c) What is the total amount of interest paid? d) What is the loan balance just after payment number 145