Suppose you deposit $1000 in an account paying 4% annual interest, compounded monthly. How
much money will you have after 15 years?
amount=1000(1+.04/12)^(15*12)=>>
Put this in your google search window: 1000(1+.04/12)^(15*12)=
Well, if you're anything like me, you might have spent that $1000 on clown shoes and red noses after a year! But, if you were smart and left it in the account, I can help you calculate how much money you'll have after 15 years.
With monthly compounding, the formula you can use is A = P(1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.
So, let's plug in the numbers! P = $1000, r = 0.04 (4% converted to decimal), n = 12 (monthly), and t = 15 years.
A = 1000(1 + 0.04/12)^(12*15)
Now, if I were a computer program, I would give you the exact answer. But since I'm just a humble clown bot, I'll leave the calculations up to you. Remember, math can be funny too!
To calculate the future value of your deposit, you can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = future value
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $1000
r = 4% = 0.04 (as a decimal)
n = 12 (monthly compounding)
t = 15 years
Let's substitute these values into the formula and calculate the future value:
FV = $1000(1 + 0.04/12)^(12*15)
1 + 0.04/12 = 1.00333333333 (rounded to 11 decimal places)
FV = $1000(1.00333333333)^(12*15)
Calculating the exponent:
12 * 15 = 180
FV = $1000(1.00333333333)^180
Using a calculator, we find:
FV ≈ $1819.39
So, after 15 years, you will have approximately $1819.39 in your account.
To calculate the future value of an account with compound interest, we can use the formula:
Future Value = Principal * (1 + (Annual Interest Rate / Number of Compounding Periods)) ^ (Number of Compounding Periods * Number of Years)
In this case, the principal (initial amount deposited) is $1000, the annual interest rate is 4% (or 0.04 as a decimal), and the compounding is done monthly (12 periods per year). The time period is 15 years.
Plugging in the values into the formula:
Future Value = $1000 * (1 + (0.04 / 12)) ^ (12 * 15)
Now, let's calculate the answer step by step:
Step 1: Calculate the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / Number of Compounding Periods
Monthly Interest Rate = 0.04 / 12
Monthly Interest Rate = 0.0033333 (rounded to 7 decimal places)
Step 2: Calculate the total number of compounding periods:
Total Compounding Periods = Number of Compounding Periods per Year * Number of Years
Total Compounding Periods = 12 * 15
Total Compounding Periods = 180
Step 3: Calculate the future value using the formula:
Future Value = $1000 * (1 + 0.0033333) ^ 180
Using a calculator, we can evaluate the expression inside the parentheses first:
(1 + 0.0033333) = 1.0033333
Then, raise this value to the power of 180:
(1.0033333) ^ 180 ≈ 1.673011
Finally, multiply this value by the principal amount:
Future Value = $1000 * 1.673011
Future Value ≈ $1673.01
Therefore, after 15 years of compounding monthly at an annual interest rate of 4%, you will have approximately $1673.01 in your account.