Find the savings plan balance after 2 years with an APR of 9% and monthly payments of $200
Can someone help?
Sure, I'll give it a shot!
Oh, savings plans...they're like a magical box that takes your money and multiplies it, right? Let's do some math wizardry here.
So, we have an APR (Annual Percentage Rate) of 9%, but we need to convert that to a monthly rate. Let's imagine the APR is actually a plush bunny hopping around, and it has 12 little baby bunnies called months. So each little bunny gets 9% interest/love per year, which means each month gets 9%/12 = 0.75% of love.
Now, let's look at the monthly payments. You're putting in $200 per month, huh? That's like giving your savings plan a monthly allowance. So generous!
To calculate the balance after 2 years, we need to calculate the interest on each monthly payment and add it to the previous balance. It's like watching a snowball grow bigger and bigger as it rolls down the savings hill.
Using a financial calculator, the savings plan balance after 2 years would be approximately $5,719.
But hey, don't forget, this is just an estimate. And remember, the real magic here is in watching your money grow day by day. So keep up the good work!
Sure, I can help you with that!
To find the savings plan balance after 2 years with an Annual Percentage Rate (APR) of 9% and monthly payments of $200, you need to use the formula for compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the total balance after time t
P = the starting principal (initial balance)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the annual interest rate (APR) is 9%, so we need to convert it to a decimal by dividing it by 100:
r = 9% / 100 = 0.09
Since the monthly payments are $200, and since the interest is compounded monthly, the number of times interest is compounded per year is 12:
n = 12
The number of years is 2:
t = 2
Now we can plug in the values into the compound interest formula:
A = P(1 + r/n)^(nt)
A = 200(1 + 0.09/12)^(12*2)
Calculating inside the parentheses first:
1 + 0.09/12 = 1.0075
A = 200(1.0075)^(24)
Calculating the value inside the parentheses next:
(1.0075)^24 ≈ 1.191022
Finally, calculating the total balance after 2 years:
A = 200 * 1.191022 ≈ $238.20
So, the savings plan balance after 2 years with an APR of 9% and monthly payments of $200 would be approximately $238.20.
Of course! I can certainly help you with that.
To calculate the savings plan balance after 2 years with an APR (Annual Percentage Rate) of 9% and monthly payments of $200, we'll need to use the formula for calculating the future value of an ordinary annuity.
The formula for calculating the future value is:
FV = P * [((1 + r)^n) - 1] / r
Where:
FV = Future Value (the savings plan balance after 2 years)
P = Monthly payment ($200 in this case)
r = Monthly interest rate (APR / 12, in decimal form)
n = Number of periods (the number of months, 2 years = 24 months)
Now, let's plug in the numbers and calculate the future value:
r = 0.09 / 12 = 0.0075 (monthly interest rate)
n = 2 years * 12 months/year = 24 (number of months)
FV = $200 * [((1 + 0.0075)^24) - 1] / 0.0075
Using a calculator, you can evaluate this expression to find the savings plan balance after 2 years with an APR of 9% and monthly payments of $200.
i = .09/12 = .0075
n = 2(12) = 24
now use the "amount of an annuity" formula, which you must have in your text or in your class notes