A family invested $4,000 and paying 6% compounded monthly, how much is in the account after 5 months.
value= 4000(1+.06/12)^5
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4000(1+.06/12)^5
To calculate the amount of money in the account after 5 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the principal amount (initial investment)
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 $4,000, the annual interest rate (r) is 6% (which is 0.06 as a decimal), the interest is compounded monthly (n = 12), and the time (t) is 5 months (which is 5/12 in years because we are using the interest rate per year).
Plugging in the given values into the formula:
A = 4000(1 + 0.06/12)^(12*(5/12))
Simplifying the equation:
A = 4000(1 + 0.005)^(5)
Now, let's calculate it step by step:
A = 4000(1.005)^(5)
A = 4000(1.027542927)
A ≈ 4110.17
After rounding to two decimal places, the family's account balance would be approximately $4,110.17 after 5 months.