$24,000 is invested for 3 years with an APR of 2% and daily compounding. Balance in the account after 3. years is $ ___
constant compounding formula is:
A = P e^r t
here
r = .02
t = 3
A = 24,000 e^(.06)
= 24,000 * 1.06283
= $ 25,484.08
Compounding daily use 365 days
Are you using a business calculator?
If you are 2% goes into I
Your N is 3
24,000 is your Principal Value (PV)
0 PMT
P/Y = 1
C/Y = 365 * (I am not 100% on this)
Calculate FV
To find the balance in the account after 3 years with daily compounding, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount in the account
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $24,000
r = 2% = 0.02 (as a decimal)
n = 365 (since interest is compounded daily)
t = 3 years
Plugging the values into the formula, we have:
A = 24000(1 + 0.02/365)^(365*3)
Calculating the values inside the parentheses:
A = 24000(1 + 0.000054)^1095
Calculating the exponent:
A = 24000(1.000054)^1095
Calculating the final amount, rounded to two decimal places:
A ≈ $25,429.52
Therefore, the balance in the account after 3 years with daily compounding is approximately $25,429.52.
To calculate the balance in the account after three years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (balance)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is $24,000, the APR (annual interest rate) is 2% (or 0.02 as a decimal), and the investment is compounded daily.
Since the interest is compounded daily, we need to adjust the values of r and n. The annual interest rate (r) needs to be divided by 365 to convert it to a daily rate, and the number of times compounded per year (n) would be 365.
Let's calculate the balance:
A = 24000(1 + 0.02/365)^(365*3)
Now, let's solve the equation step by step:
Step 1: Calculate the daily interest rate: 0.02 / 365 = 0.00005479452
Step 2: Calculate the exponent: 365 * 3 = 1095
Step 3: Calculate the parenthesis inside the formula: (1 + 0.00005479452) = 1.00005479452
Step 4: Calculate the final balance: 24000 * (1.00005479452)^1095
Using a calculator or a programming language:
A ≈ 24000 * (1.00005479452)^1095 ≈ 24000 * 1.06845569412 ≈ 25682.94
Therefore, the balance in the account after three years would be approximately $25,682.94.