Problem $5-3$ Compound Interest $($LO$1)$Problem $5-29$ Annuities $($LO$3)$

You can buy a car that is advertised for $$20,520$ on the following terms: $($a$)$ pay $$20,520$ and receive a $$5,520$ rebate from th

manufacturer; $($b$)$ pay $$570$ a month for $3$ years for total payments of $$20,520,$ implying zero percent financing.

a$.$ Calculate the present value of the payments for option $($a$)$ if the interest rate is $1\mathrm{.}25\%$ per month.

Present value

b$.$ Calculate the present value of the payments for option $($b$)$ if the interest rate is $1\mathrm{.}25\%$ per month.

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Present value

Suppose that the value of an investment in the stock market has increased at an average compound rate of about $5\%$ since $1909.$ It is

now $2020.$

Note: For all requirements, do not round intermediate calculations. Round your answer to $2$ decimal places.

a$.$ If your great$-$grandfather invested $$1,000$ in $1909,$ how much would that investment be worth today?

b$.$ If an investment in $1909$ has grown to $$1$ million, how much was invested in $1909?$