Question 125490
Parts a and b of your problem are just plugging in numbers and doing the arithmetic.  For a, put 1 in for n, 5 in for t, and convert 8% to a decimal, namely 0.08, and put that in for r.


For b, same thing, except you put in 4 for n.


You can punch numbers on a calculator as well as I can so I'll leave that part to you.


Part c asks about the difference between compounding annually or quarterly.  Let's look at an example.  Say you had $1000 in the bank at 4% for one year.
At the end of a year of annual compounding, you would have $1040, or a $40 yield.  But if it was quarterly compounding, at the end of the first quarter, they would pay 1% or $10, so you would have $1010.  At the end of the second quarter you would receive another 1% interest, but paid against the new $1010 balance, so you would get an interest payment of $10.10 making your balance $1020.10.  The next quarter your interest payment would be $10.201 and the balance would be $1030.301, and the last quarter, you would get $10.303, for a balance of $1040.602, or $.60 better than you did compounding annually.  In general, the more frequently you compound, the greater the yield for a given rate of annual interest -- that's because you are being paid interest on interest already earned.


Part d.  You left off the formula, but it is {{{A=Pe^(rt)}}}.  Just remember the word PERT.  {{{rt=.04*5=0.2}}}.  If you use the calculator built in to Windows, turn on the scientific mode, click the INV checkbox, click the 1 key, click the ln function key, (you should have the value for e - 2.7183...), multiply, 0.2,multiply,2000.  You should get roughly $2442.81


Part e.  

Start with {{{A=Pe^(rt)}}}


We want to solve for t when A = 2P, so


{{{2P=Pe^(rt)}}}


{{{2=e^(rt)}}}


{{{log(e,2)=log(e,e^(rt))}}}


{{{log(e,2)=rt*log(e,e)}}}, but {{{log(e,e)=1}}}, so


{{{log(e,2)=rt}}}


and finally {{{t=log(e,2)/r}}}


For a rate of 8%, {{{t=log(e,2)/.08}}}


On the Windows calculator, press 2, press the ln (ln means {{{log(e,x)}}})function key, divide, .08, equals roughly 8.66.


There is a quick way to approximate the time it takes for money to double.  You divide 72 by the interest rate as a whole number.  In this case 72/8 = 9 -- way close enough if you need to do the calculation quickly in your head.