Simple and compound interest

Question

if you paid $54 to a loan company for the use of 1087 for 115 days what annual rate of interest did they charge (assume a 360 day year

Answer 1

Let S = amount of money at the end of the period

S_o = amount of money invested

I = interest rate

t = time

Then,

S = S_o(1 + I)^t = 1,141 = 1087(1 + I)^(.3194) or 1.049678 = (1 + I)^(.3194)

Taking the logarithm of both sides: .021 = (.3194)log(1 + I) .0659 = log(1 + I)

1.16386 = 1 + I or I = .1639 or 16.39% interest