Morew Unit $3$A Assiennent: Modelling Exponentials & Flnance

PART Z: FINANCE: Expectation C$3$

Narne:

This ossignment will be personalized to YoU using any combinotion of the digits in your student af to generote the parameters needed for each question $($le$,5$ amounts ond$/$or Interest rotes$).$ At the BE GINNING of coch "stoge" you will be told how to determine whot these A$\text{'}$s will be and you MUST write them down in the oppropriate column of the chort provided BEFORE answering the question. You must show All calculations $($including the formula you chose to use$)$ for EA CH question for full morks.

STAGE $1$: INVESTING IN AN ANNUITY

You are trying to save a substantial amount of money to put towards a down payment on a new automobile four years from now. After consultation with your financial advisor, you decided to save $\}q,$ annual interest rate compounded monthly. $q,$ every month in a bank account which offers $q,$

What is the amount of the annuity at the end of $4$ years?

$[2$ marks$]$

How much less will the annuity be worth if you decided to wait a year to begin investing $($i$.$e$.,$ you will only invest for three years?$).$

marks$]$

STAGE $2$: PURCHASING A NEW AUTOMOBILE

Take half the amount from your four$-$year annuity in stage $1$ and use it as a down payment for the purchase of a new car. Your down payment will be $ $q,$ You can afford to make $ $q,$ bi$-$weekly payments over five years towards your new automobile. The car dealership is offering $\%$ financing for the $5-$year term, compounded bi$-$weekly. $q,$ amount$)$

How much interest in total will you pay on this car loan over the course of the loan period?

$[2$ mark