Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly.
What is the future value of this annuity after 10th payment? [
interest per month = 6/12 = 0.5% = 0.005
every month multiply by 1.005
every month also add 200
in the end
200 * (1.005^10 - 1) /.005
= 2045.61
The interest gained us about 46 in less than a year.
To find the future value of an annuity, we can use the formula for the future value of a series of equal periodic payments:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity
P = Payment amount
r = Interest rate per compounding period
n = Number of compounding periods
In this case, the payment amount (P) is Rs. 200, the interest rate (r) is 6% per year or 0.06/12 = 0.005 per month (since it is compounded monthly), and we want to find the future value after the 10th payment, so the number of compounding periods (n) is 10.
Now, let's calculate the future value:
FV = 200 * [(1 + 0.005)^10 - 1] / 0.005
FV = 200 * (1.005^10 - 1) / 0.005
To simplify this calculation, we can use an online calculator or a spreadsheet program. Plugging in the values, we find:
FV ≈ Rs. 2,417.63
Therefore, the future value of this annuity after the 10th payment is approximately Rs. 2,417.63