i do not understand

Question

Use the numbers from the original example: $1,000 invested at a 2% interest rate compounded n times per year. Compare the change in P as n increases. Fill in the table. Use a calculator and write the values to 5 decimal places.

n
1 (once per year) a0
4 (every 3 months) a1
12 (every month) a2
52 (every week) a3
365 (every day) a4

 

p=p0(1+r/n)^n

Answer 1

Use a scientific calculator (so order if operations is performed properly)

 

Please note that 2%/interest will need to be entered as a decimal,  .02

Compound interest, that is banks take the 2% for the year & for example (for 1/2 the year) they give you 1% interest, then for the second 1/2 of the year they give you the "other 1/2", the difference between this and Simple interest, is once you have interest its Yours and the bank will ADD it before calculating interest again...

Fortunately, there is a formula (given) we can use instead of doing multiple calculations (thus the exponent, for the repeated multiplication)...

 

 

P0- is his much you start with, - I'm on my phone, I needed to get on my computer.. ( i'll edit on a bit)

 

P₀= 1000   r = 0.02 or just .02      n = (this is what they want you to change and do 5 calculations & compare the END result.)

 

1.  Once a year (just simple interest -->  1000*(1+.02/1) ^1 = 1000*(1 + .02)  = 1000 *(1.02) => _________

 

2. 4 times a year n = 4 -->  1000(1+ .02/4)^4   (MAKE SURE YOU USE ()'s!!! and it is BEST to do 1-calculation, type it ALL in and calculate)....     1000 "(" 1 "+" ".02" "/" 4 ")" "^" 4  "="

 

you should get...   $1020.1505006  ~ 1020.15050  (5-dec)

 

3. 12 times a year, n = 12  -->   1000*(1 + .02/12)^12  = ______________

 

4. 52 times a year, n = 52 -->   1000 * (1 + .02/52)^52 = _____________

 

5.  365 times/"daily"   n = 365 -->  1000 * (1 + .02/365)^365 = __________

 

Note: this will be very close to the "P*e^(rt) " continuous/exponential growth, ...

 

Message me, and I'll check your answers... :-)

 

I'm also available for tutoring (online too at discounted rate)

 

 

 

*Thanks for the Additional Comment on the Actual Formula-- but.. IF n = # of times PER YEAR, then t is # of YEARS...

 

 

(n*t)  IS the Actual # of How many times the Calculation is Done.

 

For 1- year, it is just n*1 or n

FOr 2 years, it is n* 2   (for Quarterly, n = 4, for 2 years, that would be a Total of 8 times, so your exponent would be 8....

 

For 5 years, at Quarterly,  n*t = 4*5= 20