$*$PLEASE SHOW THE FORMULAS USED$***$

QUESTION $1$

What is the present value of an investment which pays a lump sum of $$50,000$ in $12$ years to an investor who requires a $6\%$ annual rate of return?

FORMATTING: Enter your answer as a positive number. Round to the nearest cent.

QUESTION $2$

If you were able to purchase the investment the investment in the previous question $($pays a $$50,000$ lump sum in $12$ years$)$ for $$20,000$ today, would annual rate of return would you

earn?

FORMATTING: Enter $"9\mathrm{.}87"$ for $9\mathrm{.}87\%.$ Round your answer to two decimal places.

QUESTION $3$

You opened an account with a $$12,000$ deposit $20$ years ago. You have made no other deposits or withdrawals. If the account has earned an $11\%$ annual rate of return, what is the

account's balance today?

FORMATTING: Enter your answer as a positive number. Round to the nearest cent

QUESTION $4$

You open an account today with a single deposit of $$10,000.$ You plan to make no other deposits or withdrawals. If the account earns an annual rate of return of $10\%,$ how many

years will it take for the account balance to grow to $$1$ million?

FORMATTING: Enter your answer as a positive number. Round to two decimal places.