if you deposit $700 a month in a savings account that earns 4% interest compounded monthly. how many months to get $3500 and what is the balance in the account.
To calculate the number of months it would take to reach $3500 in a savings account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, which is $3500 in this case.
P = the principal amount, which is $700 (the monthly deposit).
r = the annual interest rate, which is 4% (or 0.04 as a decimal).
n = the number of times that interest is compounded per year, which is 12 since it is compounded monthly.
t = the number of years (or months in this case).
Rearranging the formula, we get:
t = (log(A/P))/(n * log(1 + r/n))
Plugging in the values:
t = (log(3500/700))/(12 * log(1 + 0.04/12))
Using a calculator, we can determine that t is approximately 7.61 months. Since we cannot have a fraction of a month, we round up to 8 months.
Now, to find the balance in the account after 8 months, we will use the future value formula again.
A = P(1 + r/n)^(nt)
Since we already know the values for P, r, n, and t, we can substitute them in:
A = 700(1 + 0.04/12)^(12 * 8)
Calculating the right side of the equation gives us approximately $3,527.03. Therefore, after 8 months, the balance in the account will be around $3,527.03.