Consider the following annuity: $2000 due at the end of each year for two years,and $3000 due thereafter at the end of each year for three years.At an interest rate of 4% compounded annually,the present value of the annuity is
A) $12,487.24.
B) $11,469.37.
C) $10,541.31.
D) $10,211.37.
E) $9,583.28.

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula for the present value of an annuity:

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

where PV is the present value, A is the periodic payment, r is the interest rate per period, and n is the number of periods.

For the first two years, the payments are $2000 each, so we can use:

PV1 = 2000 * [1 - (1+0.04)^(-2)]/0.04 = $3,952.32

For the next three years, the payments are $3000 each, so we can use:

PV2 = 3000 * [1 - (1+0.04)^(-3)]/0.04 = $8,517.05

The total present value is the sum of these two present values:

PV = PV1 + PV2 = $3,952.32 + $8,517.05 = $12,469.37

Therefore, the best choice is B.

Consider the Following Annuity: $2000 Due at the End of Each