in order to accumulate enough money for a down payment on a house, a couple deposits 249$ per month into an account paying 6%compounded monthly. If payments are made at the end of each period, how much money will be in the account in 7years?
To calculate the future value of the deposits, we can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value
P is the regular deposit amount
r is the interest rate per period
n is the number of periods
In this case, the deposit amount (P) is $249, the interest rate (r) is 6%/12 = 0.005, and the number of periods (n) is 7*12 = 84.
FV = 249 * ((1 + 0.005)^84 - 1) / 0.005
FV ≈ $24,653.71
Therefore, there will be approximately $24,653.71 in the account after 7 years.
To calculate the amount of money that will be in the account in 7 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the initial deposit (monthly payment)
r = the interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the monthly payment is $249, the interest rate is 6% (or 0.06 as a decimal), interest is compounded monthly (so n = 12), and the time period is 7 years.
Using this information, we can plug in the values into the compound interest formula:
A = 249(1 + 0.06/12)^(12*7)
A = 249(1 + 0.005)^(84)
A = 249(1.005)^(84)
Now we can calculate the final amount:
A = 249(1.484852)
A ≈ $369.29
Therefore, there will be approximately $369.29 in the account after 7 years.
To find out how much money will be in the account in 7 years, we need to calculate the future value of the monthly deposits compounded monthly.
The formula for calculating the future value of an investment with regular deposits can be given as:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the investment
P is the monthly deposit amount
r is the interest rate per period (compounded monthly)
n is the total number of periods
In this case, P = $249, r = 0.06/12 (6% interest rate divided by 12 months), and n = 7*12 (7 years multiplied by 12 months per year).
Substituting the given values into the formula, we have:
FV = $249 * ((1 + 0.06/12)^(7*12) - 1) / (0.06/12)
Now let's calculate this value.
FV = $249 * ((1 + 0.005)^(84) - 1) / 0.005
FV = $249 * (1.005^84 - 1) / 0.005
FV = $249 * (1.500357 - 1) / 0.005
FV = $249 * 0.500357 / 0.005
FV = $249 * 100.0714
FV ≈ $24,917.36
Therefore, there will be approximately $24,917.36 in the account after 7 years.