Time Value of Money After Being Continuous Compounded

Please see the attachment.
11. What is the future value in three years of $1,000 invested in an account with a stated annual interest rate of 8%,

(a). Compounded annually?
(b). Compounded semiannually?
(c.). Compounded monthly?
(d). Compounded continuously?
(e). Why does the future value increase as the compounding period shortens?

12. Compute the future value of $1,000 continuously compounded for

(a). 5 years at a stated interest rate of 12 percent.
(b). 3 years at a stated interest rate of 12 percent.
(c). 10 years at a stated interest rate of 12 percent.
(d). 8 years at a stated interest rate of 12 percent.

13. Investment Corporation of America has an unfunded pension liability of $800 million that must be paid in 20 years. To assess the value of the firms' stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 9.5 percent, what is the present value of this liability?

14. John Johnson recently inherited $10,000 and wants to buy a car in five years. John estimates that the car will cost $16,105 at that time. What interest rate must he earn to be able to afford the car?

4a) How much money must be invested today at 5% compoundedcontinuously so that in 10 years it is worth $10000?
4b) How long will it take $X to triple at an interest rate of 8% compoundedcontinuously?

Starting at age 25, you deposit $2000 a year into an IRA account for retirement. Treat the yearly deposits into the account as a continuous income stream. If money in the account earns 6%, compoundedcontinuously, how much will be in the account 40 years later, when you retire at age 65? How much of the final amount is interest?

Russ McClelland, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 7% compounded quarterly. Another offers 6.75% compoundedcontinuously.
1. Growth of an account: If Russ chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $80,000?
2. Doub

a. What amount of money should you put in the bank today so that you will have $12,000 at the end of six years if you can earn 8% compounded annually?
b. How much money should you save annually so that you will have $1500 after eight years if you can earn 9% compounded annually?
c. What interest rate would allow you to ac

Money is transferred continuously into an account at the constant rate of $2,400 per year. The account earns interest at the annual rate of 6% compoundedcontinuously. How much will be in the account at the end of 5 years?

Someone who is 22 years old wins a prize of 5000$. He invests the money at 8% compounded quarterly for 43 years until he retires. When he retires he invests the money at 7% compounded monthly and makes equal monthly withdrawals for further 25 years at which time the money would ran out. How much money would he get each month?

Which amounts represents the end value of investing $80,000 for 3 years at a continuously compounded rate of 12%?
I am not sure how to calculate a problem which has continuous compounding - I know you have to use the e function, but I do not understand or know how.. Can I just substitute the value of e into the forumla?

I am in Pre-Calc and we are covering the number e and the function e^x. I do not understand how to compound continuously. Please explain how to do this. Here is my problem: Suppose you invest $1.00 at 6% annual interest. Calculate the amount that you would have after one year if the interest is compoundedcontinuously.

1. A bank pays 2.5% per year on its savings account, while a money market account pays 2.4% per year compoundedcontinuously. The bank's rate is:
a. Lower than the money market rate.
b. Equivalent to the money market rate.
c. Higher than the money market rate, but by less than 0.10%.
d. Greater than the money market r