pre calc question

Question

A savings account pays interest at a annual percentage rate (APR) of 2.1%, compounded daily.

A customer opens a savings account with an initial deposit of $2000. Assuming no further deposits or withdrawals, after how many years will the value of the account reach $2600?

Round your answer to three decimal places.

Answer: The value will reach $2600 after  years.

Answer 1

A = P(1+r/n)^nt

where P=2000= starting amount

A=2600= ending amount

r=.021= rate of annual interest, APR

n=365.25= number of compounding periods per year

t = years = about 12.495

2600/2000=1.3= e^.021t

t = ln1.3/.021 = 12.494 years with continuous compounding

1.3 = (1.021)t

t = ln1.3/ln1.021 = 12.6 years with annual compounding