We need to determine if the problem relates to an ordinary annuity or an annuity due. We are asked to calculate the amount that must be invested at the beginning of each year at 7%, compounded annually, to pay off a debt of $80,000 in 5 years.

1. Problem Description

We need to determine if the problem relates to an ordinary annuity or an annuity due.

We are asked to calculate the amount that must be invested at the beginning of each year at 7%, compounded annually, to pay off a debt of $80,000 in 5 years.

2. Solution Steps

(a) The problem states that the investment is made "at the beginning of each year". This means the payment is made at the beginning of the period, so this is an annuity due.

(b) We need to find the payment amount (PMT) for an annuity due.

The future value of an annuity due is given by:

$FV = PMT * \frac{(1+i)^n - 1}{i} * (1+i)$

where:

$FV$ is the future value of the annuity

$PMT$ is the payment amount

$i$ is the interest rate per period

$n$ is the number of periods

In this case, we have:

$FV = 80000$

$i = 0.07$

$n = 5$

We want to find $PMT$. We can rearrange the formula to solve for $PMT$:

$PMT = \frac{FV}{\frac{(1+i)^n - 1}{i} * (1+i)}$

$PMT = \frac{FV * i}{((1+i)^n - 1) * (1+i)}$

Plugging in the values, we get:

$PMT = \frac{80000 * 0.07}{((1+0.07)^5 - 1) * (1+0.07)}$

$PMT = \frac{5600}{((1.07)^5 - 1) * (1.07)}$

$PMT = \frac{5600}{(1.4025517307 - 1) * 1.07}$

$PMT = \frac{5600}{(0.4025517307) * 1.07}$

$PMT = \frac{5600}{0.4307303518}$

$PMT = 12999.79125$

Rounding to the nearest cent, we get $12999.79$.

3. Final Answer

Annuity due

$12999.79