2. On the first day of each month, starting January 1,1995 , Smith deposits 100 in an account earning nominal interest i(12)=0.09, with interest credited the last day of each month. In addition, Smith deposits 1000 in the account every December 31. On what day does the account first exceed 100,000? 3. Find the present value at time t=0 of an n-year continuous annuity based on force of interest t=p+1+rests where p,r,s are constants. 4. Show that an amortized loan amount n at interest rate i per period can be repaid by the series of n geometrically increasing payments K1=(1+i),K2=(1+i)2,,Kn=(1+i)n, with the first payment made one period after the loan. Show that the outstanding balance at time t=Bt=(nt)(1+i)t 5. The borrower of a loan of $10,000 makes monthly interest payments to the lender at rate i(12)=0.15, and monthly deposits of 100 to a sinking fund earning i(12)=0.09. When the sinking fund reaches 10,000 the borrower will repay the principal and discharge the loan. Fins the total amount paid by the borrower over the course of the loan