Question

An annuity pays out $4000 at the beginning of each year in perpetuity. If the interest is 5% compounded annually, find:

a.The present value of the whole annuity:

A) $80,000
B) $60,000
C) $100,000
D) $50,000 b. The present value of the annuity for payments received, starting from the end of the 30th year:

A) $0
B) $4,000
C) $20,000
D) $16,000

Answer 1

The present value of the whole annuity is $80,000. The present value of the annuity for payments received, starting from the end of the 30th year, is $16,000.

Step-by-step explanation:

To find the present value of the whole annuity, we can use the formula:

PV = PMT / r

Where PV is the present value, PMT is the annuity payment, and r is the interest rate.

In this case, the annuity payment is $4000 and the interest rate is 5%. Plugging these values into the formula, we get:

PV = 4000 / 0.05 = $80,000

Therefore, the present value of the whole annuity is $80,000.

For the present value of the annuity for payments received, starting from the end of the 30th year, we can use the formula:

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

Where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.

In this case, the annuity payment is $4000, the interest rate is 5%, and the number of periods is 30. Plugging these values into the formula, we get:

PV = 4000 / ((1+0.05)^30 -1) = $16,000

Therefore, the present value of the annuity for payments starting from the end of the 30th year is $16,000.