If you have a savings of $2235 and deposit the amount into an account that pays 2% annual interest, compounded monthly, what is the balance in the account after 4 years?
4 years = 48 months
interest/month = .02/12 = .00166666666
so every month multiply by 1.001666666
2235 * 1.001666666666^48 = 2420.99
or about 2421.
To calculate the balance in the account after 4 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial savings)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year (monthly compounding means n = 12)
t = number of years the money is invested for
Given:
P = $2235
r = 2% = 0.02
n = 12
t = 4
Plugging the values into the formula:
A = 2235(1 + 0.02/12)^(12*4)
A = 2235(1 + 0.00167)^(48)
Using a calculator, we can find:
A ≈ $2352.354
Therefore, the balance in the account after 4 years will be approximately $2352.35.
To calculate the balance in the account after 4 years, we can use the formula for compound interest. The formula is:
A = P(1 + r/n)^(n*t)
Where:
A = the final account balance
P = the initial principal amount (savings)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, the initial principal amount (P) is $2235, the annual interest rate (r) is 2% (2% expressed as a decimal is 0.02), the interest is compounded monthly (12 times per year, so n = 12), and the time period (t) is 4 years.
Plugging these values into the formula, we have:
A = 2235(1 + 0.02/12)^(12*4)
Simplifying this expression, we get:
A = 2235(1 + 0.00167)^(48)
Now we can calculate the value inside the parentheses:
A = 2235(1.00167)^(48)
Using a calculator, we can evaluate this expression:
A ≈ 2235(1.090852)
A ≈ 2432.03
Therefore, the balance in the account after 4 years would be approximately $2432.03.