If 5000 is deposited at the end of every year for 10 years at 5% compounded monthly, then the amount of this annuity on the date of the last payment is
To calculate the amount of this annuity on the date of the last payment, we need to 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 of the annuity
P = Payment amount per period
r = Interest rate per period
n = Number of periods
In this case, the payment amount per period (P) is $5000, the interest rate per period (r) is 5% compounded monthly, and the number of periods (n) is 10 (since the annuity lasts for 10 years).
First, we need to convert the annual interest rate to a monthly interest rate. Since the interest is compounded monthly, we divide the annual interest rate by 12.
Monthly interest rate (r) = 5% / 12 = 0.05 / 12 = 0.0041667
Next, we compute the future value of the annuity using the formula mentioned above:
FV = 5000 * [(1 + 0.0041667)^120 - 1] / 0.0041667
Calculating this equation will give you the amount of the annuity on the date of the last payment.