You deposit $200 into an account earning 5%, compounded monthly. How much will be in the account after 2 years?
To calculate the amount in the account after 2 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the 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 = $200
r = 5% = 0.05 (as a decimal)
n = 12 (monthly compounding)
t = 2 years
Let's substitute the values into the formula and calculate the final amount:
A = 200(1 + 0.05/12)^(12*2)
1 + 0.05/12 ≈ 1.004167 (rounding to 6 decimal places)
A ≈ 200(1.004167)^(12*2)
A ≈ 200(1.004167)^24
A ≈ 200 * 1.105171 (rounded to 6 decimal places)
A ≈ $221.03
Therefore, after 2 years, there will be approximately $221.03 in the account.
To calculate the amount in the account after 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $200, the annual interest rate (r) is 5% (or 0.05 as a decimal), the interest is compounded monthly (n = 12 times per year), and the number of years (t) is 2.
Plugging these values into the formula, we have:
A = 200(1 + 0.05/12)^(12*2)
Now we can calculate the final amount:
A = 200(1 + 0.00417)^(24)
A = 200(1.00417)^(24)
A ≈ 220.41
Therefore, the amount in the account after 2 years will be approximately $220.41.
following the same procedure I showed you earlier, you would have
amount = 200(1.05)^2
= ....