Question $1$:

This is a two part problem. The following series of payments will repay a present sum of $$6000$ at an $8\%$

interest rate. First, explain why this is the case. Second, find the present sum that is equivalent to this,

series of payments with a $10\%$ interest rate $($i$.$e$.,$ apply discount factors to determine the NPV of the future

payments at a $10\%$ interest rate$).$

Question $2$:

This is a two part problem. Part $1$: Bill makes a loan to a neighbor of $$15,000($i$.$e$.,$ the principal of the

loan is $$15,000).$ The neighbor agrees to pay back the principal of the loan over $5$ years in $5$ equal

payments at the end of each year. In addition, the neighbor agrees to pay $10\%$ simple interest on the

unpaid principal each year. What is the amount of each of the five payments the neighbor will make?

Part $2,$ suppose Bill's actual discount rate for money is $6\%.$ What is the present value of the payments the

neighbor will make to Bill?

Question $3$:

How much must you invest now at $8\mathrm{.}3\%$ interest to accumulate $$100,000$ in $51$ years?

Question $4($FE Review$)$:

The need for a large$-$capacity water system is forecast to occur $4$ years from now. At that time, the

system required is estimated to cost $$40,000.$ If an account earns $12\%$ per year compounded annually, the

amount that must be placed in the account at the end of each year in order to accumulate the necessary

purchase price is most nearly:

$($a$)$ $$8,000$

$($b$)$ $$8,370$

$($c$)$ $$9,000$

$($d$)$ $$10,000$

Show work as part of your answer!