9600 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 37800 dollars?

lt will take 28.09 years for the account value to reach $37800

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:

A = P (1 + r) t

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r = Annual Nominal Interest Rate (decimal form)

Replacing with the values given

37800= 9600 (1+0.05)^t

Solving for t (years)

37800/9600 = 1.05^t

3.9375 = 1.05^t

log 3.9375 = log 1.05^t

log 3.9375 = t (log 1.05)

log 3.9375/log 1.05 = t

t = 28.09 years

final answer is : )