Step By step! # 15

Question

How much money will be in an account at the end of 5 years if $2,000 is deposited at 6% intrest compounded 2 times per year? Assume no deposits or withdrawls are made

Answer 1

The compound interest formula is:

 

A_end = A_start (1+r)ⁿ

 

A_end = Final amount

A_start = Starting amount

r = interest rate per period as a decimal, not a percent

n = number of periods

 

The tricky part about this is that the "period" is actually 6 months, because the compounding is done twice a year. 

 

So the interest applied every 6 months is 1/2 the annual interest, or 3%.

And the total number of periods is 10, because there are 2 6-month periods per year -- and over 5 years that makes 10 periods.

 

So:

 

A_start = 2000

r = 3% or 0.03

n = 10

 

So plug the numbers in:

 

A_end = 2000 * (1 + .03)¹⁰

 

The result is $2687.83