To calculate the present value of the annuity, use the present value formula. Multiply the present value by (1+r) to calculate the present value of an annuity due. To calculate the future value of the annuity, use the future value formula. Multiply the future value by (1+r) to calculate the future value of an annuity due.
a. To calculate the present value of the payments in the form of an ordinary annuity, we can use the formula:
Present Value = Payment imes \left(1 - \dfrac{1}{(1+r)^n}\right) \div r
Where:
- Payment is the amount received each year ($25,000)
- r is the interest rate (12% or 0.12)
- n is the number of years (8)
Substituting the values into the formula:
Present Value = $25,000 \times \left(1 - \dfrac{1}{(1+0.12)^8}\right) \div 0.12
Calculating this expression will give you the present value of the payments.
b. To calculate the present value if the payments are an annuity due, we simply need to multiply the present value calculated in part a by (1+r).
c. To calculate the future value if the payments are an ordinary annuity, we can use the formula:
Future Value = Payment \times \left(\left(1+r\right)^n - 1\right) \div r
Substituting the given values into the formula will give you the future value.
d. To calculate the future value if the payments are an annuity due, we can multiply the future value calculated in part c by (1+r).