Question

Makayla invested $630 in an account paying an interest rate of 5.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,860?

Answer 1

19.7 or 20 rounded

Explanation:

A = $ 1,861.65

A = P + I where

P (principal) = $ 630.00

I (interest) = $ 1,231.65

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / e^rt

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r