Answer:
Explanation:
AI-generated answer
a. To calculate how much Jose would need to deposit in the account each month, we can use the future value of an ordinary annuity formula.
The future value of an ordinary annuity formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = future value
P = monthly deposit
r = interest rate per period
n = number of periods
In this case, Jose wants to have $800,000 in 30 years, and the interest rate is 6%. Since the interest rate is stated annually, we need to convert it to a monthly rate by dividing it by 12.
r = 6% / 12 = 0.06 / 12 = 0.005
We also need to multiply the number of years by 12 to get the number of periods.
n = 30 years * 12 = 360 periods
Now, we can substitute the values into the formula and solve for P:
800,000 = P * [(1 + 0.005)^360 - 1] / 0.005
Simplifying the equation:
800,000 = P * [2.2080403 - 1] / 0.005
800,000 = P * 1.2080403 / 0.005
800,000 = 241,608.06P
Dividing both sides of the equation by 241,608.06:
P = 800,000 / 241,608.06
P ≈ $3,310.43
Therefore, Jose would need to deposit approximately $3,310.43 in the account each month.
b. To calculate how much total money Jose will put into the account, we can multiply the monthly deposit by the number of periods.
Total money = Monthly deposit * Number of periods
Total money = $3,310.43 * 360
Total money ≈ $1,190,552.80
Therefore, Jose will put approximately $1,190,552.80 into the account.
c. To calculate how much total interest Jose will earn, we can subtract the total money deposited from the total future value.
Total interest = Total money - Total money deposited
Total interest = $800,000 - $1,190,552.80
Total interest ≈ -$390,552.80
Jose will not earn any interest, but rather have a shortfall of approximately $390,552.80.