If you invested a penny on Jan 1,1776 at 10% interest compounded daily, how much would you have on jan 1 2011?
There are 85775 days
rate = .10/365 = .0002739.. (I stored it in memory)
amount = 1(1.0002739...)^85775
= 1.60148.. x 10^10
about 16 billion pennies
or about $160,148,327
um sorry but it should be 0.01(1.0002)^85775 instead right?
To calculate the future value of an investment with daily compounding interest, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $0.01 (initial investment)
r = 10% = 0.10 (as a decimal)
n = 365 (daily compounding)
t = 2011 - 1776 = 235 (number of years)
Now let's calculate the future value (A):
A = 0.01(1 + 0.10/365)^(365*235)
Calculating this, the future value of the investment would be approximately $193,735,416,813,252,147,726,592,663,580,941,375,141,371,554,872,418,819,782,035,696,472,207,426,120,961,093.
To calculate the final amount you would have by January 1, 2011, if you invested a penny on January 1, 1776, with a 10% interest rate compounded daily, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case:
P = $0.01 (a penny)
r = 10% = 0.10 (as a decimal)
n = 365 (daily compounding)
t = 2011 - 1776 = 235 years
Plugging these values into the formula:
A = $0.01(1 + 0.10/365)^(365*235)
To calculate this, you can use a calculator or a spreadsheet software like Excel.