You deposit $250 each month into an account
earning 3.5% interest compounded monthly.
Part A, how much will you have in the account in 30 years?
Round to the nearest cent.
To answer this question,
we will use the annuity formula shown here below,
where A is the account balance after t years,
PMT is the regular deposit amount,
r is the annual interest rate as a decimal,
n is the number of compounds per year
and t is the time in years.
Because we're looking for the account balance in 30 years,
we are trying to determine A,
where A, the account balance after 30 years
is equal to this quotient,
where we have PMT in the numerator,
PMT is the regular deposit amount, which in our case is $250
and now we have times
and then in parentheses we have the quantity
one plus r divided by n raised to the power of nt,
where r is the annual interest rate as a decimal,
the interest rate is 3.5%
and therefore r is 0.035,
this is divided by n, the number of compounds per year,
the interest is compounded monthly and therefore n is 12
and the sum is raised to the power of n times t,
where n is 12 and t is the time in years
and therefore t is 30
and then we have minus one, close parenthesis,
divided by r divided by n,
which gives us 0.035
divided by 12.
When we're evaluating a complicated fraction
or a quotient on the calculator,
we should include parentheses
around the numerator and denominator,
so let's include a set of parentheses around the numerator
and notice how we already have parentheses
around the denominator.
Now we go to the calculator and enter the quotient.
We have open parenthesis, 250,
open parenthesis, open parenthesis
and then one plus 0.035
divided by 12, close parenthesis,
this is raise the power of 12 times 30, which is 360,
so we press the exponent key
and we can enter 360 or we can enter 12 times 30,
let's enter 12 times 30
and now we press the right arrow to exit the exponent
and then we have minus one and then close parenthesis
and then another close parenthesis for the numerator
and then we have divided by in parentheses,
0.035 divided by 12
and enter.
To the nearest cent, the account balance is $158,853.19.
So now we know in 30 years,
the account balance will be again, $158,853.19.
Part B, how much total money will you put into the account,
when you deposit $250 each month for 30 years
and therefore the total money put into the account
is $250 times the number of months in 30 years,
which is 30 times 12,
which is equal to 250 times 360,
which is equal to $90,000.
And for part C, how much total interest will you earn?
To determine the interest earned,
we take the account balance for 30 years
and subtract the total money you put into the account,
which is $90,000.
So we have 158,853.19
minus 90,000,
which is equal to $68,853.19.
So this is the amount of interest you earned
over the 30 year period.
I hope you found this helpful.