Suppose $500 is deposited into an account that earns 6.5% annual interest and no more deposits or withdrawals are made.o
What is balance in 1 year
1 month
29 M0nths
after t years, you will have
500(1+.065)^t
just convert months to years if needed.
If the interest is credited at the end of the year, only multiples of 12 months have any effect.
To calculate the balance in the account after a certain period of time, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = balance after time t
P = initial deposit
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = time (in years)
For this particular scenario:
Initial deposit (P) = $500
Annual interest rate (r) = 6.5% = 0.065 (in decimal form)
Now, to calculate the balance after 1 year:
The interest is compounded annually (n = 1), so substituting the values into the formula:
A = 500(1 + 0.065/1)^(1*1)
A = 500(1 + 0.065)^1
A = 500(1.065)
A ≈ $532.50
Therefore, the balance after 1 year is approximately $532.50.
To calculate the balance after 1 month:
Since the interest is compounded annually, we need to adjust the time (t) to represent months. Using the formula:
A = 500(1 + 0.065/1)^(1/12)
A = 500(1 + 0.065)^(1/12)
A = 500(1.0054167)
A ≈ $502.71
Therefore, the balance after 1 month is approximately $502.71.
To calculate the balance after 29 months:
Using the formula:
A = 500(1 + 0.065/1)^(1*(29/12))
A = 500(1 + 0.065)^(29/12)
A = 500(1.2535004)
A ≈ $626.75
Therefore, the balance after 29 months is approximately $626.75.
To find the balance at different time periods, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the ending balance
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the time in years
Given that $500 is deposited into an account that earns 6.5% annual interest, we can calculate the balances as follows:
1. Balance in 1 year:
Using the formula, we have:
A = 500(1 + 0.065/1)^(1*1)
A = 500(1 + 0.065)^1
A = 500(1.065)
A = $532.50
Therefore, the balance after 1 year is $532.50.
2. Balance in 1 month:
Since interest is compounded annually, we need to adjust the time to match the compounding period. In this case, we are looking for the balance after 1/12 of a year (1 month). Therefore, t = 1/12.
Using the formula, we have:
A = 500(1 + 0.065/1)^(1/12*1)
A = 500(1 + 0.065)^(1/12)
A = 500(1.0054)
A = $502.70
Therefore, the balance after 1 month is $502.70.
3. Balance in 29 months:
Using the formula, we have:
A = 500(1 + 0.065/1)^(1/12*29)
A = 500(1 + 0.065)^(29/12)
A = 500(1.2836)
A = $641.80
Therefore, the balance after 29 months is $641.80.