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.

Answer 1

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

Answer 2

check - should be close to continuous compounding
1.375 = e^rt
ln 1.375 = 5r
r = .0637
or
6.37% sure enough