A contractor needs to replace equipment in $7$ years. The equipment is expected to cost $$152,000.$ Assuming a nominal interest rate of $6\mathrm{.}75\%,$ determine the folfowing:

a$.$ The amount of money that needs to be saved annually to purchase the equipment.

b$.$ The amount of money that needs to be invested today to purchase the equipment if the interest is continuously compounded.

Problem $2(14$ points$)$

An engineering firm has a loan of $$500,000$ with an interest rate of $7\mathrm{.}15\%($assume it is compounded interest$)$ for $4$ years. Determine the following:

a$.$ The total amount the loan with cost $($principal and interest$)$ if there are interest only payments each year.

b$.$ The total amount the loan with cost $($principal and interest$)$ if the entire loan is paid at the end $($no intermediate payments$).$

c$.$ The total amount the loan with cost $($principal and interest$)$ if there is a constant principal payment each year.

Problem $3(22$ points$)$

A loan for $$365,000$ has a nominal interest rate of $8\mathrm{.}8\%$ per year that is compounded monthly and has a duration of $15$ years. Determine the following:

a$.$ The effective annual percentage rate $($APR$).$

b$.$ Assume that equal payments are made each month for the duration of the loan $($includes interest and loan payback$).$ Determine the payment and the total payback amount for the loan.

c$.$ Based on part b$,$ determine the amount of interest and loan payback amount for each of the first $3$ payments. Determine the amount of the loan that is still owed after $3$ payments.

d$.$ Based on part b$,$ assume that an additional $$1000$ payment is made towards the principal on each payment. Determine the amount of interest and loan payback amount for each of the first $3$ payments including the additional amount. Determine the amount of the loan that is still owed after $3$ payments.