You have 700 dollars in your bank account. Suppose your money is compounded every month at a rate of 0.5 percent per month.
(a) How much do you have after t years.
(b) How much do you have after 100 months
To calculate the amount of money you have after a certain period of time given compounding interest, you can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A is the future value of the money
P is the principal amount (initial amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Let's solve the questions step by step:
(a) How much do you have after t years?
In this scenario, the rate is 0.5 percent per month, which is equivalent to 0.005 (in decimal form). The money is compounded every month, so n = 12 (since there are 12 months in a year).
Assuming t represents the number of years, we can plug in the values into the compound interest formula:
A = 700 * (1 + 0.005/12)^(12t)
(b) How much do you have after 100 months?
To calculate the future value after 100 months, we need to find the equivalent value of t in years. Since there are 12 months in a year, 100 months is equal to 100/12 = 8.33 years.
Plug in this value into the formula:
A = 700 * (1 + 0.005/12)^(12 * 8.33)
Calculating the actual values will give you the precise amount of money you'll have after the given time periods.