Please help me solve this word problem about money increasing and compounded semiannually

Question

If $500 is deposited to an account paying 4.2% interested compounded semiannually, how long it will take for the account to increase to $900?

(Round your answer to the whole number)

Answer 1

Compound Interest formula is:

A=P(1+ R/N)^NT

A (Amount) final amount
P (Principle) starting amount
R (interest rate) in decimal form
N (number of times interest is compounded per yr)
T (time in years)

 

P= 500

R= .042

N= 2 because semiannually is 6 mon. or half a year

T= is # of years until the account is increased to 900

 

Plug the information into the formula then type it into your calculator exactly like this:

 

500(1+(.042/2))^(2*t)

 

Notice at the end of the equation I have left the last part as (2*t) we will have to use trial and error until we find the amount of years it will take for the account to increase to $900.

 

The first number of years i tried was 16, so i replace the "t" with 16 and it gave me $975.29 which is $75.29 dollars over the $900 amount we are trying to increase to.

 

So, i chose the lower number 14, and it gave me $894.73 rounding to the nearest hundredth makes 14 years the amount of time it would take for the account to reach $900.

 

ANSWER: 14