Bo has $800 that he wants to turn into $1100 in 5 years. If interest is compounded daily, calculate the interest rate he would need to make this happen.

let x = 1+r

1100 = 800 (x)^(5*365)

1.375 = x^1825

log 1.375 = 1825 log x

log x = .1383/1825 = 7.57823 *10^-5

x = 1.00017451
r = x-1 = .00017451 per day
365 r = .0637 nominal per year
= 6.37 percent

check - should be close to continuous compounding

1.375 = e^rt
ln 1.375 = 5r
r = .0637
or
6.37% sure enough

To calculate the interest rate Bo would need to achieve in order to turn $800 into $1100 in 5 years with daily compounding, we can use the formula for compound interest:

A = P*(1+r/n)^(n*t)

Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case, let's assume that Bo wants to achieve a final amount of $1100, the principal amount is $800, the number of times interest is compounded per year is 365 (daily compounding), and the number of years is 5. We need to solve for the annual interest rate r.

So, the equation becomes:

1100 = 800*(1+r/365)^(365*5)

To solve this equation for r, we need to use numerical methods or a financial calculator. We'll use an online calculator or a spreadsheet software like Microsoft Excel.

Plugging this equation into Excel or an online calculator, we will get an approximate annual interest rate.