in order to accumulate enough money for a down payment, a couple deposits $618 each month into a account paying 3% compounded monthly. if payments are made at the end of each period, how much will the account have in 6 years?
You can use the amortization formula and solve for P in the next problem.
To calculate the amount the account will have in 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial deposit amount
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years the money is compounded for
In this case, the monthly deposit is $618, and the interest rate is 3% (or 0.03) compounded monthly. The time period is 6 years.
Let's plug in the values into the formula:
P = $618 (monthly deposit)
r = 0.03 (annual interest rate)
n = 12 (compounded monthly)
t = 6 (number of years)
A = 618(1 + 0.03/12)^(12*6)
Now, we can calculate the future value of the account by solving this expression:
A = 618(1 + 0.0025)^(72)
A = 618(1.0025)^(72)
A = 618 * (1.194357865)
A = $738.47 (rounded to the nearest cent)
Therefore, after 6 years of making monthly deposits of $618 into the account with a 3% interest rate compounded monthly, the account balance will be approximately $738.47.