a$.$ You decide to save $$600$ at the end of each year for

$15$ years in an account that earns an annual interest rate

of $4\%.$ Calculate the future value of this ordinary

annuity.

Future Value $($Ordinary Annuity$)$:

$(5$ Points$)$

b$.$ If instead, you make these $$600$ payments at the

beginning of each year for $15$ years $($annuity due$),$ what

will be the future value of your investment?

Future Value $($Annuity Due$)$:

Points$)$

c$.$ A friend proposes investing $$5,000$ every year for $10$

years in an account that pays a $5\%$ interest rate. Would

they have more if they invested annually $($ordinary

annuity$)$ or invested at the beginning of each year

$($annuity due$)?$ Calculate both and explain which is

more beneficial.

More Beneficial Option:

Points$)$

Loan and Interest Rate Analysis $(10$ Points$)$

a$.$ You take out a student loan for $$20,000,$ to be repaid

over $5$ years at an annual interest rate of $6\%.$ What is

the annual payment you need to make to pay off the

loan in full? $($Use the annuity formula.$)$

Annual Payment:

$(5$ Points$)$

b$.$ You have a choice between two investment options:

Option $1$: Invest $$2,000$ annually for $25$ years at a $6\%$

interest rate.

Option $2$: Invest $$2,500$ annually for $20$ years at a $5\%$

interest rate.

Calculate the future value of both options. Which option results in

a higher future value?

Higher Future Value Option:

$(5$ Points$)$