$48.$ How much interest will be earned in an account into which $$1,000$ is deposited for one

year with continuous compounding at a $13\%$ rate?

A$.$ $$130\mathrm{.}00$

B$.$ $$138\mathrm{.}83$

C$.$ $$169\mathrm{.}00$

D$.$ $$353\mathrm{.}34$

Chapter $05-$ The Time Value of Money

$5-10$

$49.$ If $$120,000$ is borrowed for a home mortgage, to be repaid at $9\%$ interest over $30$ years

with monthly payments of $$965\mathrm{.}55,$ how much interest is paid over the life of the loan?

A$.$ $$120,000$

B$.$ $$162,000$

C$.$ $$181,458$

D$.$ $$227,598$

$50.$ Prizes are often not "worth" as much as claimed. Place a value on a prize of $$5,000,000$

that is to be received in equal payments over $20$ years, with the first payment beginning today.

Assume an interest rate of $7\%.$

A$.$ $$2,833,898\mathrm{.}81$

B$.$ $$2,911,015\mathrm{.}68$

C$.$ $$2,609,144\mathrm{.}14$

D$.$ $$2,738,304\mathrm{.}13$

please explain these with formulas :)