Question

A deferred perpetuity-due begins payments at time n with annual payments of $2000 per year. If the present value of this perpetuity-due is equal to $6539.39 and the effective rate of interest i=0.13, find n. A. 3

B. 2
C. 11
D. 8
E. 9

Answer 1

The time at which the deferred perpetuity-due begins payments can be found by solving for n using the present value formula and the given present value and effective interest rate. The answer is E. 9.

Step-by-step explanation:

To find the time at which the deferred perpetuity-due begins payments, we need to calculate the future value of the perpetuity-due and then solve for n using the present value formula. The future value of the perpetuity-due can be calculated using the formula: FV = R * (1 + i)^n, where R is the annual payment, i is the effective rate of interest, and n is the number of periods. In this case, the future value is unknown, but the present value is given as $6,539.39. Using the present value formula, we can write the equation: PV = R * (1 - (1 + i)^-n) / i = $6,539.39. Solving for n, we find:

n = -log(1 - (PV * i / R)) / log(1 + i) = 9,

Therefore, the correct answer is E. 9.