What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,800 at the end of Year 4 if the interest rate is 5%?
A) $11,881.98
B) $11,104.66
C) $12,881.40
D) $9,327.91
E) $12,215.12

Question

Quizplus · Accepted Answer

This problem requires calculating the present value of both the annuity and the lump sum at the end of Year 4 and then adding them together. To calculate the present value of the annuity, we can use the formula:

PV = (A/i) x (1 - 1/(1+i)^n)

where PV is the present value, A is the annual payment, i is the interest rate, and n is the number of payments. Plugging in the values, we get:

PV = (2,250/0.05) x (1 - 1/(1+0.05)^4)
PV = $7,314.89

To calculate the present value of the lump sum at the end of Year 4, we can use the formula:

PV = FV/(1+i)^n

where FV is the future value, i is the interest rate, and n is the number of periods. Plugging in the values, we get:

PV = 3,800/(1+0.05)^4
PV = $3,789.77

Adding these two values together, we get:

PV = 7,314.89 + 3,789.77
PV = $11,104.66

Therefore, the best choice is B.

What's the Present Value of a 4-Year Ordinary Annuity of $2,250