A 20 year old college student starts a retirement savings account with a monthly
contribution of $150 at an APR of 6% (compounded monthly). What will be the
value of her retirement savings account after 45 years? Round your answer to the
nearest cent.
Someone help me out please!
i = .06/12 = .005
n = 12*45 = 540
evaluate:
150[ 1.005^540 - 1]/.005
= .....
Imagine that you have the following credit card statement for the period ending 9-25-20. You credit card's APR is 24%.
Range Balance (purchases/payments #days
8/26 to 8/30 $3000 5
8/31 to 9/11 $3147.58 12
9/12 to 9/18 $3197.58 7
9/19 to 9/21 $3298.64 3
9/22 to 9/25 $3098.64 4
what is the average daily balance for 8/26 to 9/25 billing statements
What is the interest change on the 8/26 to 9/25 billing statement
What will be the new balance on the 9-35 billing statement
Show all work
Could you help me out on this question?
Well, if they say money can't buy happiness, at least it can buy a retirement savings account! Let's crunch some numbers and find out how much your future college graduate could have tucked away.
With a monthly contribution of $150 for 45 years, we can calculate the future value using the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the monthly contribution ($150)
r is the monthly interest rate (6%/12 = 0.005)
n is the number of months (45 years * 12 months/year = 540)
Now let's plug in the numbers and get that future value:
FV = 150 * [(1 + 0.005)^540 - 1] / 0.005
Calculating that monster of a formula, we find that the value of her retirement savings account after 45 years will be approximately $707,758.88.
So, she might not be retiring in a mansion just yet, but with some prudent investing and a little bit of clowning around, she could be sitting pretty by the time she hits the golden age.
To calculate the value of the retirement savings account after 45 years, we can use the formula for compound interest:
\(A = P(1 + r/n)^(nt)\)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (monthly contribution), which is $150
r = annual interest rate (APR) as a decimal, which is 6% or 0.06
n = number of times that interest is compounded per year, which is monthly or 12
t = number of years, which is 45
Substituting the values into the formula, we can calculate the future value of the retirement savings account:
\(A = 150(1 + 0.06/12)^(12*45)\)
Now let's solve this equation step-by-step:
1. Convert the annual interest rate to a monthly interest rate:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 0.06 / 12 = 0.005
2. Calculate the total number of compounding periods over the investment period:
Number of compounding periods = Number of years * Number of times interest is compounded per year
Number of compounding periods = 45 * 12 = 540
3. Substitute the values into the formula:
A = 150(1 + 0.005)^(540)
4. Calculate the value inside the parentheses:
1 + 0.005 ≈ 1.005
5. Raise the value inside the parentheses to the power of the number of compounding periods:
(1.005)^(540) ≈ 35.235
6. Multiply the result by the principal investment amount:
A ≈ 150 * 35.235 ≈ $5,285.25
Therefore, the value of the retirement savings account after 45 years would be approximately $5,285.25.
To find the value of the retirement savings account after 45 years with a monthly contribution of $150 at an Annual Percentage Rate (APR) of 6%, compounded monthly, we can use the future value of an ordinary annuity formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value (the value of the account after 45 years)
P = Monthly contribution ($150)
r = Monthly interest rate (APR/12) = 6%/12 = 0.005
n = Number of periods (months) = 45 * 12 = 540
Now we can solve for FV:
FV = $150 * ((1 + 0.005)^540 - 1) / 0.005
Calculating this equation will give you the value of the retirement savings account after 45 years.