You deposit $300 each month into an account earning 5% interest compounded monthly.

a) How much will you have in the account in 25 years?

$

b) How much total money will you put into the account?

c) How much total interest will you earn?

a) Well, you've got your monthly deposit of $300 and an interest rate of 5%, compounded monthly. After 25 years, you'll end up with... drumroll, please... a grand total of $185,472.12 in your account! That's a lot of zeroes!

b) Let's do some math here, shall we? You're depositing $300 each month for 25 years, which means you'll put a total of $90,000 into the account. It's like holding a never-ending magic show of money!

c) Now, let's calculate the total interest you'll be earning. Over 25 years, the interest on your monthly deposits will add up to about $95,472.12. That's quite a hefty sum, isn't it? Who knew that clowning around with money could be this profitable?

To calculate the answers, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Total amount after time t
P = Initial deposit amount
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years

Given:
P = $300
r = 5% = 0.05 (as a decimal)
n = 12 (compounded monthly)
t = 25 years

a) To calculate the total amount in the account after 25 years, we use the formula:

A = 300(1 + 0.05/12)^(12*25)

A = 300(1 + 0.004166667)^(300)

Using a calculator, the value of A is approximately $120,317.11.

b) To calculate the total money put into the account, we multiply the monthly deposit amount by the number of months:

Total Money = Monthly Deposit * Number of Months

Total Money = $300 * 12 * 25

Total Money = $90,000

c) To calculate the total interest earned, we subtract the total money put into the account from the total amount in the account:

Total Interest = Total Amount - Total Money

Total Interest = $120,317.11 - $90,000

Total Interest = $30,317.11

To find the answers to these questions, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount after t years,
P = the initial amount (principal),
r = the annual interest rate (as a decimal),
n = the number of times interest is compounded per year, and
t = the number of years.

a) To find out how much you will have in the account after 25 years, we need to calculate A.

Given:
P = $300 (monthly deposit),
r = 5% (interest rate as a decimal = 0.05),
n = 12 (compounded monthly),
t = 25 (number of years).

First, let's convert the monthly deposit into an annual deposit:
Annual deposit = Monthly deposit * 12 = $300 * 12 = $3600.

Now, we can use the formula to find A:
A = 3600(1 + 0.05/12)^(12*25)
A ≈ $11,101.41

Therefore, you will have approximately $11,101.41 in the account after 25 years.

b) To calculate the total money put into the account, we need to multiply the monthly deposits by the number of months in 25 years.

Total money put into the account = Monthly deposit * Number of months in 25 years
Total money put into the account = $300 * 12 * 25
Total money put into the account = $90,000.

Therefore, you will have put a total of $90,000 into the account over 25 years.

c) To calculate the total interest earned, we need to subtract the total deposited amount from the final amount.

Total interest earned = Final amount - Total money put into the account
Total interest earned = $11,101.41 - $90,000
Total interest earned = -$78,898.59.

Note that the result is negative because the total deposited amount is greater than the final amount, indicating that you have earned negative interest, likely due to the low interest rate compared to the amount deposited.

Therefore, you would have earned approximately -$78,898.59 in negative interest over 25 years.

25 years = 25*12 = 300 monthly periods

interest rate monthly r = 0.05/12 = .0041666666...
so every month multiply by 1.004166666..... and add 300
formula:
v = 300 [ 1.0041666^300 - 1 ] / .004166666
= 300 [ 3.48129 -1 ] / 0.004166666
= 300 [ 595.5 ]
= 178,652.94

b.
300 * 300 = 90,000

c. subtract b from a