A bank account yields 7 percent interest, compounded annually. If you deposit $1,000 in the account, what will the account balance be after 5 years?

1 Answer
Mar 29, 2016

Answer:

#$1,402.55#

Explanation:

Your total money, after depositing #P# dollars in an account earning #r# interest per year for #t# years, is given by the formula:
#A=P(1+r)^t#

The problem has given us the following:

  • #P#, the principal amount of the deposit (how much money you start with), is #$1,000#.
  • #r#, the interest rate per year, is #7%# (which, as a decimal, is #0.07#).
  • #t#, the number of years, is #5#.

Using this info, we plug into the formula and solve:
#A=P(1+r)^t#
#A=1000(1+0.07)^5#
#A=1000(1.07)^5~~$1,402.55#

Compare this to how much money you would make without compound interest:
#A=P(rt+1)#
#A=1000(0.07*5+1)#
#A=1000(1.35)=$1,350#

You would make about #$52# less, which is why it's always better to go for a compound interest account, rather than a normal interest account.