After 35 years, the annuity will grow to approximately $163,859.64, with an interest of $107,859.64 earned, derived from periodic deposits of $800 over the specified periods.
To solve the math problem, we need to use the following formula for the future value of an annuity due:
FV = P * ((1 + r)^(n) - 1) / r * (1 + r)
where:
FV is the future value of the annuity
P is the periodic deposit
r is the interest rate per period
n is the number of periods
Plugging in the given values, we get:
FV = 800 * ((1 + 0.045/2)^(35*2) - 1) / (0.045/2) * (1 + 0.045/2)
Using a calculator, we can simplify this expression to get:
FV ≈ 163,859.64
This is the value of the annuity after 35 years.
To find the interest, we need to subtract the total deposits from the future value. The total deposits are the periodic deposit multiplied by the number of periods, which is:
800 * 35 * 2 = 56,000
Therefore, the interest is:
163,859.64 - 56,000 = 107,859.64
This is the amount of interest earned over 35 years.