a piece of machinery can be bought for 200000 cash or for 20000 down and payments of 20000 per year for 15 years. what is the annual interest rate of the time payments?

To solve this problem, we need to use the formula for the present value of an annuity:

PV = PMT * [(1 - (1 + r)^-n) / r]

Where:

• PV is the present value, or the total amount that a series of future payments is worth now;
• PMT is the periodic payment;
• r is the interest rate per period;
• n is the number of periods.

In this case, we know that:

• PV = $200,000 -$20,000 = $180,000 (the cash price minus the down payment);
• PMT = $20,000 (the annual payment);
• n = 15 years.

We need to solve for r, the annual interest rate. This is a bit tricky because r is in the denominator and as an exponent. It's not as simple as isolating r and solving for it. Instead, we'll need to use a financial calculator or a software tool that can handle this type of calculation.

If you use a financial calculator or software, you would input:

• PV = 180,000
• PMT = 20,000
• n = 15

And then solve for r. The exact steps would depend on the specific calculator or software you're using.

Please note that this calculation assumes that the payments are made at the end of each period (i.e., the end of each year). If the payments are made at the beginning of each period, the calculation would be slightly different.