You want to buy a car, and a local bank will lend you $$40,000.$ The loan will be fully amortized over $5$ years $(60$ months$),$ and the nominal interest rate will be $8\%$ with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR?

Starting next year, you will need $$5,000$ annually for $4$ years to complete your education. $($One year from today you will withdraw the first $$5,000.)$ Your uncle deposits an amount today in a bank paying $6\%$ annual interest, which will provide the needed $$5,000$ payments.

a$.$ How large must the deposit be$?$

b$.$ How much will be in the account immediately after you make the first withdrawal?

Six years from today you need $$10,000.$ You plan to deposit $$1,500$ annually, with the first payment to be made a year from today, in an account that pays a $5\%$ effective annual rate. Your last deposit, which will occur at the end of Year $6,$ will be for less than $$1,500$ if less is needed to reach $$10,000.$ How large will your last payment be$?$

Simon recently received a credit card with an $18\%$ nominal interest rate. With the card, he purchased an Apple iPhone $11$ for $$700.$ The minimum payment on the card is $$20$ per month.

a$.$ If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card?

b$.$ If Simon makes monthly payments of $$70,$ how many months will it be before he pays off the debt?

c$.$ How much more in total payments will Simon make under the $$20-$a$-$month plan than under the $570-$a$-$month plan? Make sure you use three decimal places for $N.$

FIN $3310$: Personal Finance Exam

Due Date: $\frac{12}{01}$

Your father is $50$ years old and will retire in $10$ years. He expects to live for $25$ years after he retires, until he is $85.$ Ho wants a fixed retirement income that has the same purchasing power at the time he retires as $$50,000$ has today. $($The real value of his retirement income will decline annually ater he retires.$)$ His retirement income will begin the day he retires, $10$ years from today, at which time he will receive $24$ additional annual payments, Annual inflation is expected to be $4\%.$ Ho currently has $590,000$ savech and he expects to cam $8\%$ annually on his savings. How much must he save during cach of the next $10$ years $($end$-$of year deposits$)$ to mect his retirement goal?