Guaranty income life offered an annuity that pays 6.65% compunded monthly. if deposited into this annuity every month, how much is in the account after 10 years? how much of this is interest?
To calculate the amount in the account after 10 years and the amount of interest earned, you need to use the formula for compound interest.
The compound interest formula is: A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (the amount deposited every month)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is the amount deposited every month, the annual interest rate (r) is 6.65% (or 0.0665 in decimal form), and the interest is compounded monthly, so the number of times compounded per year (n) is 12. The number of years (t) is 10.
Now, let's calculate the final amount in the account (A) after 10 years:
A = P(1 + r/n)^(nt)
= P(1 + 0.0665/12)^(12*10)
To calculate the interest earned, we subtract the principal amount from the final amount in the account:
Interest = A - P
Keep in mind that the deposit should be made every month consistently for accurate results.
Let's plug in the values and calculate:
A = P(1 + 0.0665/12)^(12*10)
Interest = A - P
Now, you can substitute the values for P, r, n, and t to find the final amount and interest earned.