Final answer:
The present value of an annuity due is found by multiplying the present value of the ordinary annuity by (1+ interest rate). In this case, the present value of the annuity due at an 8% interest rate is $6,912.
Step-by-step explanation:
The question revolves around the concept of annuities in finance, which involves a series of equal payments made at regular intervals. Specifically, it asks for the present value of an annuity due given the present value of an ordinary annuity and an 8% interest rate. An annuity due is similar to an ordinary annuity, except that the payments occur at the beginning of each period rather than the end.
To calculate the present value of an annuity due, we can take the present value of the ordinary annuity and multiply it by (1+i), where i is the interest rate (8% in this case). The formula reflects the fact that each payment for an annuity due is received one period sooner, which means its present value must be adjusted to account for the extra period of compounding.
Present Value of Annuity Due = Present Value of Ordinary Annuity × (1 + i)
Using the given values, the calculation would be:
Present Value of Annuity Due = $6,400 × (1 + 0.08)
Present Value of Annuity Due = $6,400 × 1.08
Present Value of Annuity Due = $6,912