Suppose that when your friend was born, your friends parents deposited $2000 in an account paying 4.5% interest, compounded monthly. What will the account balance be after 18 years?
To find the account balance after 18 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final account balance
P is the principal amount (initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this scenario:
P = $2000
r = 4.5% = 0.045 (4.5% divided by 100 to convert to decimal)
n = 12 (compounded monthly)
t = 18 years
Now we can plug in the values:
A = $2000(1 + 0.045/12)^(12*18)
A = $2000(1 + 0.00375)^(216)
A = $2000(1.00375)^(216)
A ≈ $2000(1.8888888889)
A ≈ $3777.78
Therefore, the account balance will be approximately $3777.78 after 18 years.
To calculate the account balance after 18 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final account balance
P = the initial deposit
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial deposit (P) is $2000, the annual interest rate (r) is 4.5% (or 0.045 as a decimal), the interest is compounded monthly (n = 12), and the investment period (t) is 18 years.
Now, let's calculate the final account balance:
A = 2000(1 + 0.045/12)^(12*18)
= 2000(1 + 0.00375)^(216)
= 2000(1.00375)^(216)
To find the final account balance, we just need to evaluate this expression:
A ≈ 2000 * 1.98665657
A ≈ $3,973.31
So, the account balance will be approximately $3,973.31 after 18 years.
To calculate the account balance after 18 years, we will use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the future account balance
P = the initial deposit amount
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $2000
r = 4.5% = 0.045 (converted to decimal form)
n = 12 (compounded monthly)
t = 18 years
Plugging in the values, we get:
A = 2000(1 + 0.045/12)^(12*18)
A = 2000(1 + 0.00375)^(216)
A = 2000(1.00375)^(216)
Calculating this, the account balance after 18 years will be approximately $4,462.39.