A father is now planning a savings program to put his daughter through college. She just celebrated

her $13$th birthday, she plans to enroll at the university in $5$ years when she turns $18$ years old, and

she should graduate in $4$ years. Currently, the annual cost $($for everything $-$ food, clothing, tuition,

books, transportation, and so forth$)$ is $$15,000,$ but these costs are expected to increase by $5\%$

annually. The college requires that this amount be paid at the start of the school year. She now has

$$7,500$ in a college savings account that pays $6\%$ annually.

a$)$ How large must each payment be if the father makes five equal annual deposits into her

account; the first deposit today and the fifth deposit on the daughter's $17$ th birthday?

Hint:

Calculate the education cost $($inflated at $5\%)$ for each year of college.

Find Total Education liability at $t=5$ : calculate the total PV of yearly costs, discounted

at $6\%,$ as of the day she enters college.

Calculate the FV $($at $t=5)$ of the initial savings of $$7,500.$

Funding Deficit at $t=5$ Total Education liability $(t=5)-FV$ of $$7,500$ savings $($at

$t=5).$

Future savings by father: Calculate deposit $($PMT$)$ per year such that the $FV{A}_{\text{d}\text{u}\text{e}}$ of the

$5-$yearly deposit at $t=5.$

b$)$ Alternatively, another option is to finance the $4-$year education costs with a $15-$year

education loan. First, they can borrow $($education$)$ funds needed at the beginning of each

year at $10\%$ p$.$a$.$ nominal interest, compounded monthly. Second, they would need to repay

the loan back annually over $15$ years, with the $1$ st loan repayment due one$-$year after

graduation $($at $t=10).$ Compute the $($end$-$of$-$period$)$ yearly payments needed to service the

loan.

Hint:

Find EAR on the loan.

Find Total Loan Outstanding $($owing to bank$)$ upon graduation $($at $t=9)$

Calculate the $15$ yearly repayments $($PMT$)$ needed to service the total

outstanding loan $($in step $2).$